#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 4 - Triangles

Chapter 5 - Trigonometric Ratios

Chapter 6 - Trigonometric Identities

Chapter 7 - Statistics

Chapter 8 - Quadratic Equations

Chapter 9 - Arithmetic Progression

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Trigonometry

Chapter 13 - Probability

Chapter 14 - Co-Ordinate Geometry

Chapter 15 - Areas Related to Circles

Chapter 16 - Surface Areas and Volumes

## Chapter 8 - Quadratic Equations

#### Page 0

Check whether the following is quadratic equation or not.

*x*^{2} + 6*x* − 4 = 0

Check whether the following is quadratic equation or not.

*x*^{2} + 6*x* − 4 = 0

Check whether the following is quadratic equation or not.

`sqrt(3x^2)-2x+1/2=0`

Check whether the following is quadratic equation or not.

`sqrt(3x^2)-2x+1/2=0`

Check whether the following is quadratic equation or not.

`x^2+1/x^2=5`

Check whether the following is quadratic equation or not.

`x^2+1/x^2=5`

Check whether the following is quadratic equation or not.

`x-3/x=x^2`

Check whether the following is quadratic equation or not.

`x-3/x=x^2`

Check whether the following is quadratic equation or not.

`2x^2-sqrt(3x)+9=0`

Check whether the following is quadratic equation or not.

`2x^2-sqrt(3x)+9=0`

Check whether the following is quadratic equation or not.

`x^2 - 2x - sqrtx - 5 = 0`

Check whether the following is quadratic equation or not.

`x^2 - 2x - sqrtx - 5 = 0`

Check whether the following is quadratic equation or not.

3*x*^{2} - 5*x* + 9 = *x*^{2} - 7*x* + 3

Check whether the following is quadratic equation or not.

3*x*^{2} - 5*x* + 9 = *x*^{2} - 7*x* + 3

Check whether the following is quadratic equation or not.

`x+1/x=1`

Check whether the following is quadratic equation or not.

`x+1/x=1`

Check whether the following is quadratic equation or not.

*x*^{2} - 3*x* = 0

Check whether the following is quadratic equation or not.

*x*^{2} - 3*x* = 0

Check whether the following is quadratic equation or not.

`(x+1/x)^2=3(1+1/x)+4`

Check whether the following is quadratic equation or not.

`(x+1/x)^2=3(1+1/x)+4`

Check whether the following is quadratic equation or not.

(2𝑥 + 1)(3𝑥 + 2) = 6(𝑥 − 1)(𝑥 − 2)

Check whether the following is quadratic equation or not.

(2𝑥 + 1)(3𝑥 + 2) = 6(𝑥 − 1)(𝑥 − 2)

Check whether the following is quadratic equation or not.

`x+1/x=x^2`, x ≠ 0

Check whether the following is quadratic equation or not.

`x+1/x=x^2`, x ≠ 0

Check whether the following is quadratic equation or not.

16*x*^{2} − 3 = (2*x* + 5) (5*x* − 3)

Check whether the following is quadratic equation or not.

16*x*^{2} − 3 = (2*x* + 5) (5*x* − 3)

Check whether the following is quadratic equation or not.

(*x* + 2)^{3} = *x*^{3} − 4

Check whether the following is quadratic equation or not.

(*x* + 2)^{3} = *x*^{3} − 4

Check whether the following is quadratic equation or not.

x(x + 1) + 8 = (x + 2) (x - 2)

Check whether the following is quadratic equation or not.

x(x + 1) + 8 = (x + 2) (x - 2)

In the following, determine whether the given values are solutions of the given equation or not:

x^{2} - 3x + 2 = 0, x = 2, x = -1

In the following, determine whether the given values are solutions of the given equation or not:

x^{2} - 3x + 2 = 0, x = 2, x = -1

In the following, determine whether the given values are solutions of the given equation or not:

x^{2} + x + 1 = 0, x = 0, x = 1

In the following, determine whether the given values are solutions of the given equation or not:

x^{2} + x + 1 = 0, x = 0, x = 1

In the following, determine whether the given values are solutions of the given equation or not:

`x^2 - 3sqrt3x+6=0`, `x=sqrt3`, `x=-2sqrt3`

In the following, determine whether the given values are solutions of the given equation or not:

`x^2 - 3sqrt3x+6=0`, `x=sqrt3`, `x=-2sqrt3`

In the following, determine whether the given values are solutions of the given equation or not:

`x+1/x=13/6`, `x=5/6`, `x=4/3`

In the following, determine whether the given values are solutions of the given equation or not:

`x+1/x=13/6`, `x=5/6`, `x=4/3`

In the following, determine whether the given values are solutions of the given equation or not:

2x^{2} - x + 9 = x^{2} + 4x + 3, x = 2, x =3

In the following, determine whether the given values are solutions of the given equation or not:

2x^{2} - x + 9 = x^{2} + 4x + 3, x = 2, x =3

In the following, determine whether the given values are solutions of the given equation or not:

`x^2-sqrt2x-4=0`, `x=-sqrt2`, `x=-2sqrt2`

In the following, determine whether the given values are solutions of the given equation or not:

`x^2-sqrt2x-4=0`, `x=-sqrt2`, `x=-2sqrt2`

In the following, determine whether the given values are solutions of the given equation or not:

a^{2}x^{2} - 3abx + 2b^{2} = 0, `x=a/b`, `x=b/a`

In the following, determine whether the given values are solutions of the given equation or not:

a^{2}x^{2} - 3abx + 2b^{2} = 0, `x=a/b`, `x=b/a`

In the following, find the value of *k* for which the given value is a solution of the given equation:

7x^{2} + kx - 3 = 0, `x=2/3`

In the following, find the value of *k* for which the given value is a solution of the given equation:

7x^{2} + kx - 3 = 0, `x=2/3`

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} - x(a + b) + k = 0, x = a

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} - x(a + b) + k = 0, x = a

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} - x(a + b) + k = 0, x = a

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} - x(a + b) + k = 0, x = a

In the following, find the value of *k* for which the given value is a solution of the given equation:

`kx^2+sqrt2x-4=0`, `x=sqrt2`

In the following, find the value of *k* for which the given value is a solution of the given equation:

`kx^2+sqrt2x-4=0`, `x=sqrt2`

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} + 3ax + k = 0, x = -a

In the following, find the value of *k* for which the given value is a solution of the given equation:

x^{2} + 3ax + k = 0, x = -a

If *x* = 2/3 and *x* = −3 are the roots of the equation *ax*^{2} + 7*x* + *b* = 0, find the values of *a*and *b*.

If *x* = 2/3 and *x* = −3 are the roots of the equation *ax*^{2} + 7*x* + *b* = 0, find the values of *a*and *b*.

Determine if, 3 is a root of the equation given below:

`sqrt(x^2-4x+3)+sqrt(x^2-9)=sqrt(4x^2-14x+16)`

Determine if, 3 is a root of the equation given below:

`sqrt(x^2-4x+3)+sqrt(x^2-9)=sqrt(4x^2-14x+16)`

#### Page 0

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, form the quadratic equation fo find x.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, form the quadratic equation fo find x.

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 1 1 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 1 1 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic eqiation to find the speed of the train.

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic eqiation to find the speed of the train.

#### Page 0

Solve the following quadratic equations by factorization:

(*x* − 4) (*x *+ 2) = 0

Solve the following quadratic equations by factorization:

(*x* − 4) (*x *+ 2) = 0

Solve the following quadratic equations by factorization:

(2*x* + 3)(3*x* − 7) = 0

Solve the following quadratic equations by factorization:

(2*x* + 3)(3*x* − 7) = 0

Solve the following quadratic equations by factorization:

4x^{2} + 5x = 0

Solve the following quadratic equations by factorization:

4x^{2} + 5x = 0

Solve the following quadratic equations by factorization:

9*x*^{2} − 3*x* − 2 = 0

Solve the following quadratic equations by factorization:

9*x*^{2} − 3*x* − 2 = 0

Solve the following quadratic equations by factorization:

6x^{2} - x - 2 = 0

Solve the following quadratic equations by factorization:

6x^{2} - x - 2 = 0

Solve the following quadratic equations by factorization:

6*x*^{2} + 11*x* + 3 = 0

Solve the following quadratic equations by factorization:

6*x*^{2} + 11*x* + 3 = 0

Solve the following quadratic equations by factorization:

5*x*^{2} - 3*x* - 2 = 0

Solve the following quadratic equations by factorization:

5*x*^{2} - 3*x* - 2 = 0

Solve the following quadratic equations by factorization:

48*x*^{2} − 13*x* − 1 = 0

Solve the following quadratic equations by factorization:

48*x*^{2} − 13*x* − 1 = 0

Solve the following quadratic equations by factorization:

3*x*^{2} = -11*x* - 10

Solve the following quadratic equations by factorization:

3*x*^{2} = -11*x* - 10

Solve the following quadratic equations by factorization:

25x(x + 1) = -4

Solve the following quadratic equations by factorization:

25x(x + 1) = -4

Solve the following quadratic equations by factorization:

`10x-1/x=3`

Solve the following quadratic equations by factorization:

`10x-1/x=3`

Solve the following quadratic equations by factorization:

`2/2^2-5/x+2=0`

Solve the following quadratic equations by factorization:

`2/2^2-5/x+2=0`

Solve the following quadratic equations by factorization:

`4sqrt3x^2+5x-2sqrt3=0`

Solve the following quadratic equations by factorization:

`4sqrt3x^2+5x-2sqrt3=0`

Solve the following quadratic equations by factorization:

`sqrt2x^2-3x-2sqrt2=0`

Solve the following quadratic equations by factorization:

`sqrt2x^2-3x-2sqrt2=0`

Solve the following quadratic equations by factorization:

a^{2}x^{2} - 3abx + 2b^{2} = 0

Solve the following quadratic equations by factorization:

a^{2}x^{2} - 3abx + 2b^{2} = 0

Solve the following quadratic equations by factorization:

`x^2-(sqrt2+1)x+sqrt2=0`

Solve the following quadratic equations by factorization:

`x^2-(sqrt2+1)x+sqrt2=0`

Solve the following quadratic equations by factorization:

`x^2-(sqrt3+1)x+sqrt3=0`

Solve the following quadratic equations by factorization:

`x^2-(sqrt3+1)x+sqrt3=0`

Solve the following quadratic equations by factorization:

4x^{2} + 4bx - (a^{2} - b^{2}) = 0

Solve the following quadratic equations by factorization:

4x^{2} + 4bx - (a^{2} - b^{2}) = 0

Solve the following quadratic equations by factorization:

ax^{2} + (4a^{2} - 3b)x - 12ab = 0

Solve the following quadratic equations by factorization:

ax^{2} + (4a^{2} - 3b)x - 12ab = 0

Solve the following quadratic equations by factorization:

`(x-1/2)^2=4`

Solve the following quadratic equations by factorization:

`(x-1/2)^2=4`

Solve the following quadratic equations by factorization:

`x^2-4sqrt2x+6=0`

Solve the following quadratic equations by factorization:

`x^2-4sqrt2x+6=0`

Solve the following quadratic equations by factorization:

`(x+3)/(x+2)=(3x-7)/(2x-3)`

Solve the following quadratic equations by factorization:

`(x+3)/(x+2)=(3x-7)/(2x-3)`

Solve the following quadratic equations by factorization:

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

Solve the following quadratic equations by factorization:

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

Solve the following quadratic equations by factorization:

`(x+3)/(x-2)-(1-x)/x=17/4`

Solve the following quadratic equations by factorization:

`(x+3)/(x-2)-(1-x)/x=17/4`

Solve the following quadratic equations by factorization:

`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3

Solve the following quadratic equations by factorization:

`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3

Solve the following quadratic equations by factorization:

`1/(x-2)+2/(x-1)=6/x` , x ≠ 0

Solve the following quadratic equations by factorization:

`1/(x-2)+2/(x-1)=6/x` , x ≠ 0

Solve the following quadratic equations by factorization:

`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1

Solve the following quadratic equations by factorization:

`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1

Solve the following quadratic equations by factorization:

`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1

Solve the following quadratic equations by factorization:

`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1

Solve the following quadratic equations by factorization:

3x^{2} − 14x − 5 = 0

Solve the following quadratic equations by factorization:

3x^{2} − 14x − 5 = 0

Solve the following quadratic equations by factorization:

`m/nx^2+n/m=1-2x`

Solve the following quadratic equations by factorization:

`m/nx^2+n/m=1-2x`

Solve the following quadratic equations by factorization:

`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`

Solve the following quadratic equations by factorization:

`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`

Solve the following quadratic equations by factorization:

`1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)=1/6`

Solve the following quadratic equations by factorization:

`1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)=1/6`

Solve the following quadratic equations by factorization:

`(x-5)(x-6)=25/(24)^2`

Solve the following quadratic equations by factorization:

`(x-5)(x-6)=25/(24)^2`

Solve the following quadratic equations by factorization:

`7x + 3/x=35 3/5`

Solve the following quadratic equations by factorization:

`7x + 3/x=35 3/5`

Solve the following quadratic equations by factorization:

`a/(x-a)+b/(x-b)=(2c)/(x-c)`

Solve the following quadratic equations by factorization:

`a/(x-a)+b/(x-b)=(2c)/(x-c)`

Solve the following quadratic equations by factorization:

x^{2} + 2ab = (2a + b)x

Solve the following quadratic equations by factorization:

x^{2} + 2ab = (2a + b)x

Solve the following quadratic equations by factorization:

(a + b)^{2}x^{2} - 4abx - (a - b)^{2} = 0

Solve the following quadratic equations by factorization:

(a + b)^{2}x^{2} - 4abx - (a - b)^{2} = 0

Solve the following quadratic equations by factorization:

a(x^{2} + 1) - x(a^{2} + 1) = 0

Solve the following quadratic equations by factorization:

a(x^{2} + 1) - x(a^{2} + 1) = 0

Solve the following quadratic equations by factorization:

x^{2} - x - a(a + 1) = 0

Solve the following quadratic equations by factorization:

x^{2} - x - a(a + 1) = 0

Solve the following quadratic equations by factorization:

`x^2+(a+1/a)x+1=0`

Solve the following quadratic equations by factorization:

`x^2+(a+1/a)x+1=0`

Solve the following quadratic equations by factorization:

abx^{2} + (b^{2} - ac)x - bc = 0

Solve the following quadratic equations by factorization:

abx^{2} + (b^{2} - ac)x - bc = 0

Solve the following quadratic equations by factorization:

a^{2}b^{2}x^{2} + b^{2}x - a^{2}x - 1 = 0

Solve the following quadratic equations by factorization:

a^{2}b^{2}x^{2} + b^{2}x - a^{2}x - 1 = 0

Solve the following quadratic equations by factorization:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4

Solve the following quadratic equations by factorization:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4

Solve the following quadratic equations by factorization:

`3x^2-2sqrt6x+2=0`

Solve the following quadratic equations by factorization:

`3x^2-2sqrt6x+2=0`

Solve the following quadratic equations by factorization:

`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5

Solve the following quadratic equations by factorization:

`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5

Solve the following quadratic equations by factorization:

`1/x-1/(x-2)=3` , x ≠ 0, 2

Solve the following quadratic equations by factorization:

`1/x-1/(x-2)=3` , x ≠ 0, 2

Solve the following quadratic equations by factorization:

`x-1/x=3` , x ≠ 0

Solve the following quadratic equations by factorization:

`x-1/x=3` , x ≠ 0

Solve the following quadratic equations by factorization:

`x-1/x=3` , x ≠ 0

Solve the following quadratic equations by factorization:

`x-1/x=3` , x ≠ 0

Solve the following quadratic equations by factorization:

`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7

Solve the following quadratic equations by factorization:

`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7

#### Page 0

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

`x^2-4sqrt2x+6=0`

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

`x^2-4sqrt2x+6=0`

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^{2} – 7x + 3 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^{2} – 7x + 3 = 0

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

3x^{2} + 11x + 10 = 0

3x^{2} + 11x + 10 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* – 4 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* – 4 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* + 4 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2*x*^{2} + *x* + 4 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square `4x^2 + 4sqrt3x + 3 = 0`

Find the roots of the following quadratic equations, if they exist, by the method of completing the square `4x^2 + 4sqrt3x + 3 = 0`

`sqrt2x^2-3x-2sqrt2=0`

`sqrt2x^2-3x-2sqrt2=0`

`sqrt3x^2+10x+7sqrt3=0`

`sqrt3x^2+10x+7sqrt3=0`

`x^2-(sqrt2+1)x+sqrt2=0`

`x^2-(sqrt2+1)x+sqrt2=0`

x^{2} - 4ax + 4a^{2} - b^{2} = 0

x^{2} - 4ax + 4a^{2} - b^{2} = 0

#### Page 0

Write the discriminant of the following quadratic equations:

2*x*^{2} - 5*x* + 3 = 0

Write the discriminant of the following quadratic equations:

*x*^{2} + 2*x* + 4 = 0

Write the discriminant of the following quadratic equations:

(*x* − 1) (2*x* − 1) = 0

Write the discriminant of the following quadratic equations:

*x*^{2} - 2*x* + *k* = 0, *k* ∈ R

Write the discriminant of the following quadratic equations:

`sqrt3x^2+2sqrt2x-2sqrt3=0`

Write the discriminant of the following quadratic equations:

*x*^{2} - *x* + 1 = 0

Write the discriminant of the following quadratic equations:

3x^{2} + 2x + k = 0

Write the discriminant of the following quadratic equations:

4x^{2} - 3kx + 1 = 0

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

16*x*^{2} = 24*x* + 1

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

*x*^{2} + *x* + 2 = 0

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

`sqrt3x^2+10x-8sqrt3=0`

3*x*^{2} - 2*x* + 2 = 0

`2x^2-2sqrt6x+3=0`

3a^{2}x^{2} + 8abx + 4b^{2} = 0, a ≠ 0

`3x^2+2sqrt5x-5=0`

*x*^{2} - 2*x* + 1 = 0

`2x^2+5sqrt3x+6=0`

`sqrt2x^2+7x+5sqrt2=0`

`2x^2-2sqrt2x+1=0`

3*x*^{2} - 5*x* + 2 = 0

Solve for *x*

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`; x ≠ 2, 4

Solve for *x*

`1/x - 1/(x-2)=3`, x ≠ 0, 2

Solve for *x*

`x+1/x=3`, x ≠ 0

#### Page 0

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them

2x^{2} - 3x + 5 = 0

Find the nature of the roots of the following quadratic equation. If the real roots exist, find them

2x^{2} - 3x + 5 = 0

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them

2*x*^{2} - 6*x* + 3 = 0

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them

2*x*^{2} - 6*x* + 3 = 0

Determine the nature of the roots of the following quadratic equation:

`3/5x^2-2/3x+1=0`

Determine the nature of the roots of the following quadratic equation:

`3/5x^2-2/3x+1=0`

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;

`3x^2 - 4sqrt3x + 4 = 0`

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them;

`3x^2 - 4sqrt3x + 4 = 0`

Determine the nature of the roots of the following quadratic equation:

`3x^2-2sqrt6x+2=0`

Determine the nature of the roots of the following quadratic equation:

`3x^2-2sqrt6x+2=0`

Determine the nature of the roots of the following quadratic equation:

(x - 2a)(x - 2b) = 4ab

Determine the nature of the roots of the following quadratic equation:

(x - 2a)(x - 2b) = 4ab

Determine the nature of the roots of the following quadratic equation:

9a^{2}b^{2}x^{2} - 24abcdx + 16c^{2}d^{2} = 0

Determine the nature of the roots of the following quadratic equation:

9a^{2}b^{2}x^{2} - 24abcdx + 16c^{2}d^{2} = 0

Determine the nature of the roots of the following quadratic equation:

2(a^{2} + b^{2})x^{2} + 2(a + b)x + 1 = 0

Determine the nature of the roots of the following quadratic equation:

2(a^{2} + b^{2})x^{2} + 2(a + b)x + 1 = 0

Determine the nature of the roots of the following quadratic equation:

(b + c)x^{2} - (a + b + c)x + a = 0

Determine the nature of the roots of the following quadratic equation:

(b + c)x^{2} - (a + b + c)x + a = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

*kx*^{2} + 4x + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

*kx*^{2} + 4x + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

`kx^2-2sqrt5x+4=0`

Find the values of *k* for which the roots are real and equal in each of the following equation:

`kx^2-2sqrt5x+4=0`

Find the values of *k* for which the roots are real and equal in each of the following equation:

3x^{2} - 5x + 2k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

3x^{2} - 5x + 2k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} + kx + 9 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} + kx + 9 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

2kx^{2} - 40x + 25 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

2kx^{2} - 40x + 25 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

9x^{2} - 24x + k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

9x^{2} - 24x + k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} - 3kx + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} - 3kx + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2(5 + 2k)x + 3(7 + 10k) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2(5 + 2k)x + 3(7 + 10k) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(3k+1)x^{2} + 2(k + 1)x + k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(3k+1)x^{2} + 2(k + 1)x + k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

kx^{2} + kx + 1 = -4x^{2} - x

Find the values of *k* for which the roots are real and equal in each of the following equation:

kx^{2} + kx + 1 = -4x^{2} - x

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} + 2(k + 3)x + (k + 8) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} + 2(k + 3)x + (k + 8) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2kx + 7k - 12 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2kx + 7k - 12 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} - 2(3k + 1)x + 8k + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} - 2(3k + 1)x + 8k + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

5x^{2} - 4x + 2 + k(4x^{2} - 2x - 1) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

5x^{2} - 4x + 2 + k(4x^{2} - 2x - 1) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(4 - k)x^{2} + (2k + 4)x + 8k + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(4 - k)x^{2} + (2k + 4)x + 8k + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(2k + 1)x^{2} + 2(k + 3)x + k + 5 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(2k + 1)x^{2} + 2(k + 3)x + k + 5 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} - 2(k + 1)x + (k + 4) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

4x^{2} - 2(k + 1)x + (k + 4) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2(k + 1)x + (k + 4) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 2(k + 1)x + (k + 4) = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

k^{2}x^{2} - 2(2k - 1)x + 4 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

k^{2}x^{2} - 2(2k - 1)x + 4 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} - 2(k - 1)x + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

(k + 1)x^{2} - 2(k - 1)x + 1 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

2x^{2} + kx + 3 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

2x^{2} + kx + 3 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

kx(x - 2) + 6 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

kx(x - 2) + 6 = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 4kx + k = 0

Find the values of *k* for which the roots are real and equal in each of the following equation:

x^{2} - 4kx + k = 0

In the following determine the set of values of k for which the given quadratic equation has real roots:

2x^{2} + 3x + k = 0

In the following determine the set of values of k for which the given quadratic equation has real roots:

2x^{2} + 3x + k = 0

In the following determine the set of values of k for which the given quadratic equation has real roots:

2x^{2} + kx + 3 = 0

2x^{2} + kx + 3 = 0

2x^{2} - 5x - k = 0

2x^{2} - 5x - k = 0

kx^{2} + 6x + 1 = 0

kx^{2} + 6x + 1 = 0

x^{2} - kx + 9 = 0

x^{2} - kx + 9 = 0

2x^{2} + kx + 2 = 0

2x^{2} + kx + 2 = 0

3x^{2} + 2x + k = 0

3x^{2} + 2x + k = 0

4x^{2} - 3kx + 1 = 0

4x^{2} - 3kx + 1 = 0

2x^{2} + kx - 4 = 0

2x^{2} + kx - 4 = 0

For what value of k, (4 - k)x^{2} + (2k + 4)x + (8k + 1) = 0, is a perfect square.

For what value of k, (4 - k)x^{2} + (2k + 4)x + (8k + 1) = 0, is a perfect square.

Find the least positive value of *k* for which the equation *x*^{2} + *kx* + 4 = 0 has real roots.

Find the least positive value of *k* for which the equation *x*^{2} + *kx* + 4 = 0 has real roots.

Find the values of *k* for which the given quadratic equation has real and distinct roots:

kx^{2} + 2x + 1 = 0

Find the values of *k* for which the given quadratic equation has real and distinct roots:

kx^{2} + 2x + 1 = 0

Find the values of *k* for which the given quadratic equation has real and distinct roots:

kx^{2} + 6x + 1 = 0

Find the values of *k* for which the given quadratic equation has real and distinct roots:

kx^{2} + 6x + 1 = 0

Find the values of *k* for which the given quadratic equation has real and distinct roots:

x^{2} - kx + 9 = 0

Find the values of *k* for which the given quadratic equation has real and distinct roots:

x^{2} - kx + 9 = 0

If the roots of the equation (b - c)x^{2} + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.

If the roots of the equation (b - c)x^{2} + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.

If the roots of the equation (a^{2} + b^{2})x^{2} − 2 (ac + bd)x + (c^{2} + d^{2}) = 0 are equal, prove that `a/b=c/d`.

If the roots of the equation (a^{2} + b^{2})x^{2} − 2 (ac + bd)x + (c^{2} + d^{2}) = 0 are equal, prove that `a/b=c/d`.

If the roots of the equations ax^{2} + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b^{2} = ac.

If the roots of the equations ax^{2} + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b^{2} = ac.

If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x^{2} + 5(p + q) x− 2(p − q) = 0 are real and unequal.

If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x^{2} + 5(p + q) x− 2(p − q) = 0 are real and unequal.

If the roots of the equation (c^{2} – ab) x^{2} – 2 (a^{2} – bc) x + b^{2} – ac = 0 in x are equal, then show that either a = 0 or a^{3} + b^{3} + c^{3} = 3abc

If the roots of the equation (c^{2} – ab) x^{2} – 2 (a^{2} – bc) x + b^{2} – ac = 0 in x are equal, then show that either a = 0 or a^{3} + b^{3} + c^{3} = 3abc

Show that the equation 2(a^{2} + b^{2})x^{2} + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.

Show that the equation 2(a^{2} + b^{2})x^{2} + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.

Prove that both the roots of the equation (x - a)(x - b) +(x - b)(x - c)+ (x - c)(x - a) = 0 are real but they are equal only when a = b = c.

Prove that both the roots of the equation (x - a)(x - b) +(x - b)(x - c)+ (x - c)(x - a) = 0 are real but they are equal only when a = b = c.

If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax^{2} + bx + c = 0 and -ax^{2} + bx + c = 0 has real roots.

If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax^{2} + bx + c = 0 and -ax^{2} + bx + c = 0 has real roots.

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Find the consecutive numbers whose squares have the sum 85.

Find the consecutive numbers whose squares have the sum 85.

Divide 29 into two parts so that the sum of the squares of the parts is 425.

Divide 29 into two parts so that the sum of the squares of the parts is 425.

Two squares have sides x cm and (x + 4)cm. The sum of this areas is 656 cm2. Find the sides of the squares.

Two squares have sides x cm and (x + 4)cm. The sum of this areas is 656 cm2. Find the sides of the squares.

The sum of two numbers is 48 and their product is 432. Find the numbers?

The sum of two numbers is 48 and their product is 432. Find the numbers?

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.

Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.

Find the two consecutive natural numbers whose product is 20.

Find the two consecutive natural numbers whose product is 20.

The sum of the squares of the two consecutive odd positive integers as 394. Find them.

The sum of the squares of the two consecutive odd positive integers as 394. Find them.

The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

The sum of a numbers and its positive square root is 6/25. Find the numbers.

The sum of a numbers and its positive square root is 6/25. Find the numbers.

The sum of a number and its square is 63/4. Find the numbers.

The sum of a number and its square is 63/4. Find the numbers.

There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?

There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?

The product of two successive integral multiples of 5 is 300. Determine the multiples.

The product of two successive integral multiples of 5 is 300. Determine the multiples.

The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.

The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.

Find the consecutive even integers whose squares have the sum 340.

Find the consecutive even integers whose squares have the sum 340.

The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.

The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.

Let us find two natural numbers which differ by 3 and whose squares have the sum 117.

Let us find two natural numbers which differ by 3 and whose squares have the sum 117.

The sum of the squares of three consecutive natural numbers as 149. Find the numbers

The sum of the squares of three consecutive natural numbers as 149. Find the numbers

Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Determine two consecutive multiples of 3, whose product is 270.

Determine two consecutive multiples of 3, whose product is 270.

The sum of a number and its reciprocal is 17/4. Find the number.

The sum of a number and its reciprocal is 17/4. Find the number.

A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?

A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?

A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.

A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.

A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number

A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number

Two numbers differ by 3 and their product is 504. Find the number

Two numbers differ by 3 and their product is 504. Find the number

Two number differ by 4 and their product is 192. Find the numbers?

Two number differ by 4 and their product is 192. Find the numbers?

A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

The sum of the squares of two positive integers is 208. If the square of the large number is 18 times the smaller. Find the numbers.

The sum of the squares of two positive integers is 208. If the square of the large number is 18 times the smaller. Find the numbers.

The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

The sum of two number *a* and *b* is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers *a* and *b*.

The sum of two number *a* and *b* is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers *a* and *b*.

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.

Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.

The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

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The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?

A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?

A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.

A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.

A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?

The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

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Ashu is* x* years old while his mother Mrs Veena is *x*^{2} years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.

Ashu is* x* years old while his mother Mrs Veena is *x*^{2} years old. Five years hence Mrs Veena will be three times old as Ashu. Find their present ages.

The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.

The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.

The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.

The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

The sum of the reciprocals of Rehman's ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

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The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?

The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?

A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

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The perimeter of a rectangular field is 82 m and its area is 400 m^{2}. Find the breadth of the rectangle.

The perimeter of a rectangular field is 82 m and its area is 400 m^{2}. Find the breadth of the rectangle.

The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m^{2}, what are the length and breadth of the hall?

The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m^{2}, what are the length and breadth of the hall?

The area of a right angled triangle is 165 m^{2}. Determine its base and altitude if the latter exceeds the former by 7 m.

The area of a right angled triangle is 165 m^{2}. Determine its base and altitude if the latter exceeds the former by 7 m.

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^{2}? If so, find its length and breadth.

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^{2}? If so, find its length and breadth.

Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth

Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth

Sum of the areas of two squares is 640 m^{2}. If the difference of their perimeters is 64 m. Find the sides of the two squares.

Sum of the areas of two squares is 640 m^{2}. If the difference of their perimeters is 64 m. Find the sides of the two squares.

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A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

Two water taps together can fill a tank in `9 3/8`. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Two water taps together can fill a tank in `9 3/8`. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

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A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. one less, the cost would remain unchanged. How long is the piece?

Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?

Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic?

A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.

Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.

If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.

Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?

Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?

In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.

In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in mathematics and 4 marks less in Science. The product of his marks would have been 180. Find his marks in two subjects.

In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects

In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

#### Textbook solutions for Class 10th Board Exam

## RD Sharma solutions for Class 10th Board Exam Mathematics chapter 8 - Quadratic Equations

RD Sharma solutions for Class 10th Board Exam Maths chapter 8 (Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10th Board Exam Mathematics chapter 8 Quadratic Equations are Formula for Solving a Quadratic Equation, Roots of a Quadratic Equation, Solutions of Quadratic Equations by Completing the Square, Solutions of Quadratic Equations by Factorization, Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form, Nature of Roots, Quadratic Equations, Quadratic Equations Examples and Solutions, Quadratic Equations, Nature of Roots, Relationship Between Discriminant and Nature of Roots, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated, Quadratic Equations Examples and Solutions.

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