R.S. Aggarwal solutions for माठेमटिक्स [इंग्रजी] इयत्ता १० chapter 4 - Quadratic Equations [Latest edition]

Which of the following are quadratic equation in x? 

x² – x + 3 = 0

Which of the following are quadratic equation in x? 

`2x^2 + 5/2 x - sqrt(3) = 0`

Which of the following are quadratic equation in x? 

`sqrt(2)x^2 + 7x + 5sqrt(2) = 0`

Which of the following are quadratic equation in x? 

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

Which of the following are quadratic equation in x? 

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

Which of the following are quadratic equation in x? 

`x - 6/x = 3`

Which of the following are quadratic equation in x?

`x + 2/x = x^2`

Which of the following are quadratic equation in x? 

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

Which of the following are quadratic equation in x? 

(x + 2)³ = x³ – 8

Which of the following are quadratic equation in x?  

(2x + 3)(3x + 2) = 6(x – 1)(x – 2)

Which of the following are quadratic equation in x? 

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

Which of the following are the roots of 3x² + 2x – 1 = 0? 

–1

Which of the following are the roots of 3x² + 2x – 1 = 0?

`1/3`

Which of the following are the roots of 3x² + 2x – 1 = 0? 

`-1/2`

Find the value of k for which x = 1 is a root of the equation x² + kx + 3 = 0. Also, find the other root.

Find the values of a and b for which `x = 3/4` and x = –2 are the roots of the equation ax² + bx – 6 = 0.

Show that `x = - (bc)/(ad)` is a solution of the quadratic equation `ad^2((ax)/b + (2c)/d)x + bc^2 = 0`.

Solve the following quadratic equation:

(2x – 3) (3x + 1) = 0

Solve the following quadratic equation:

4x² + 5x = 0

Solve the following quadratic equation:

3x² – 243 = 0

Solve the following quadratic equation:

2x² + x – 6 = 0

Solve the following quadratic equation:

x² + 6x + 5 = 0

Solve the following quadratic equation:

9x² – 3x – 2 = 0

Solve the following quadratic equation:

x² + 12x + 35 = 0

Solve the following quadratic equation:

x² = 18x – 77

Solve the following quadratic equation:

6x² + 11x + 3 = 0

Solve the following quadratic equation:

6x² + x – 12 = 0

Solve the following quadratic equation:

3x² – 2x – 1 = 0

Solve the following quadratic equation:

4x² – 9x = 100

Solve the following quadratic equation:

15x² – 28 = x

Solve the following quadratic equation:

4 – 11x = 3x²

Solve the following quadratic equation:

48x² – 13x – 1 = 0

Solve the following quadratic equation:

`x^2 + 2sqrt(2)x - 6 = 0`

Solve the following quadratic equation:

`sqrt(3)x^2 + 10x - 8sqrt(3) = 0`

Solve the following quadratic equation:

`sqrt(3)x^2 + 11x + 6sqrt(3) = 0`

Solve the following quadratic equation:

`3sqrt(7)x^2 + 4x - sqrt(7) = 0`

Solve the following quadratic equation:

`sqrt(7)x^2 - 6x - 13sqrt(7) = 0`

Solve the following quadratic equation:

`4sqrt(6)x^2 - 13x - 2sqrt(6) = 0`

Solve the following quadratic equation:

`3x^2 - 2sqrt(6)x + 2 = 0`

Solve the following quadratic equation:

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

Solve the following quadratic equation:

`x^2 - 3sqrt(5)x + 10 = 0`

Solve the following quadratic equation:

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

Solve the following quadratic equation:

`x^2 + 3sqrt(3)x - 30 = 0`

Solve the following quadratic equation:

`sqrt(2)x^2 + 7x + 5sqrt(2) = 0`

Solve the following quadratic equation:

5x² + 13x + 8 = 0

Solve the following quadratic equation:

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

Solve the following quadratic equation:

9x² + 6x + 1 = 0

Solve the following quadratic equation:

100x² – 20x + 1 = 0

Solve the following quadratic equation:

`2x^2 - x + 1/8 = 0`

Solve the following quadratic equation:

`10x - 1/x = 3`

Solve the following quadratic equation:

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

Solve the following quadratic equation:

2x² + ax – a² = 0

Solve the following quadratic equation:

4x² + 4bx – (a² – b²) = 0

Solve the following quadratic equation:

4x² – 4a²x + (a⁴ – b⁴) = 0

Solve the following quadratic equation:

x² + 5x – (a² + a – 6) = 0

Solve the following quadratic equation:

x² – 2ax – (4b² – a²) = 0

Solve the following quadratic equation:

x² – (2b – 1)x + (b² – b – 20) = 0 

Solve the following quadratic equation:

x² + 6x – (a² + 2a – 8) = 0

Solve the following quadratic equation:

abx² + (b² – ac)x – bc = 0

Solve the following quadratic equation:

x² – 4ax – b² + 4a² = 0

Solve the following quadratic equation:

4x² – 2(a² + b²)x + a²b² = 0

Solve the following quadratic equation:

12abx² – (9a² – 8b²)x – 6ab = 0

Solve the following quadratic equation:

a²b²x² + b²x – a²x – 1 = 0 

Solve the following quadratic equation:

9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0

Solve the following quadratic equation:

`16/x - 1 = 15/(x + 1), x ≠ 0, -1`

Solve the following quadratic equation:

`4/x - 3 = 5/(2x + 3), x ≠ 0, -3/2`

Solve the following quadratic equation:

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

Solve the following quadratic equation:

`1/(x - 1) - 1/(x + 5) = 6/7, x ≠ 1, -5`

Solve the following quadratic equation:

`1/(2x - 3) + 1/(x - 5) = 1 1/9, x ≠ 3/2, 5`

Solve the following quadratic equation:

`1/(2a + b + 2x) = 1/(2a) + 1/b + 1/(2x)`

Solve the following quadratic equation:

`(x + 3)/(x - 2) - (1 - x)/x = 4 1/4, x ≠ 2, 0`

Solve the following quadratic equation:

`(3x - 4)/7 + 7/(3x - 4) = 5/2, x ≠ 4/3`

Solve the following quadratic equation:

`x/(x - 1) + (x - 1)/4 = 4 1/4, x ≠ 0, 1` 

Solve the following quadratic equation:

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

Solve the following quadratic equation:

`x/(x + 1) + (x + 1)/x = 2 4/15, x ≠ 0, 1`

Solve the following quadratic equation:

`(x - 4)/(x - 5) + (x - 6)/(x - 7) = 3 1/3, x ≠ 5, 7`

Solve the following quadratic equation:

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

Solve the following quadratic equation:

`1/(x - 2) + 2/(x - 1) = 6/x, x ≠ 0, 1, 2`

Solve the following quadratic equation:

`1/(x + 1) + 2/(x + 2) = 5/(x + 4), x ≠ -1, -2, -4`

Solve the following quadratic equation:

`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x ≠ -1, -1/5, -4`

Solve the following quadratic equation:

`3((3x - 1)/(2x + 3)) - 2((2x + 3)/(3x - 1)) = 5, x ≠ 1/3, -3/2` 

Solve the following quadratic equation:

`3((7x + 1)/(5x - 3)) - 4((5x - 3)/(7x + 1)) = 11, x ≠ 3/5, (-1)/7`

Solve the following equation by factorisation method:

`((4x - 3)/(2x + 1)) - 10((2x + 1)/(4x - 3)) = 3, x ≠ -1/2, 3/4`

Solve the following quadratic equation:

`(x/(x + 1))^2 - 5(x/(x + 1)) + 6 = 0, x ≠ b, a`

Solve the following quadratic equation:

`a/((x - b)) + b/((x - a)) = 2, x ≠ b, a`

Solve the following quadratic equation:

`a/((ax - 1)) + b/((bx - 1)) = (a + b), x ≠ 1/a, 1/b`

Solve the following quadratic equation:

`3^((x + 2)) + 3^(-x) = 10`

Solve the following quadratic equation:

`4^((x + 1)) + 4^((1 - x)) = 10`

Solve the following quadratic equation:

`2^(2x) - 3·2^((x + 2)) + 32 = 0`

Find the discriminant of the following equation:

2x² – 7x + 6 = 0

Find the discriminant of the following equation:

3x² – 2x + 8 = 0

Find the discriminant of the following equation:

`2x^2 - 5sqrt(2)x + 4 = 0`

Find the discriminant of the following equation:

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

Find the discriminant of the following equation:

(x – 1)(2x – 1) = 0

Find the discriminant of the following equation:

1 – x = 2x²

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – 6x + 4 = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

2x² + x – 4 = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

25x² + 30x + 7 = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

16x² = 24x + 1

Find the roots of the following equation, if they exist, by applying the quadratic formula:

15x² – 28 = x

Find the roots of the following equation, if they exist, by applying the quadratic formula:

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

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`sqrt(2)x^2 + 7x + 5sqrt(2) = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`sqrt(3)x^2 + 10x - 8sqrt(3) = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

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

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`2x^2 + 6sqrt(3)x - 60 = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`4sqrt(3)x^2 + 5x - 2sqrt(3) = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`3x^2 - 2sqrt(6)x + 2 = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`2sqrt(3)x^2 - 5x + sqrt(3) = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² + x + 2 = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

2x² + ax – a² = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

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

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`2x^2 + 5sqrt(3)x + 6 = 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

3x² – 2x + 2 = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`x + 1/x = 3, x ≠ 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`1/x - 1/(x - 2) = 3, x ≠ 0, 2`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

`x - 1/x = 3, x ≠ 0`

Find the roots of the following equation, if they exist, by applying the quadratic formula:

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

Find the roots of the following equation, if they exist, by applying the quadratic formula:

36x² – 12ax + (a² – b²) = 0 

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – 2ax + (a² – b²) = 0 

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – 2ax – (4b² – a²) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² + 6x – (a² + 2a – 8) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² + 5x – (a² + a – 6) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – 4ax – b² + 4a² = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

4x² – 4a²x + (a⁴ – b⁴) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

4x² + 4bx – (a² – b²) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – (2b – 1)x + (b² – b – 20) = 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

3a²x² + 8abx + 4b² = 0, a ≠ 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

a²b²x² – (4b⁴ – 3a⁴)x – 12a²b² = 0, a ≠ 0 and b ≠ 0

Find the roots of the following equation, if they exist, by applying the quadratic formula:

12abx² – (9a² – 8b²)x – 6ab = 0, where a ≠ 0 and b ≠ 0                  

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

2x² – 8x + 5 = 0

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

`3x^2 - 2sqrt(6)x + 2 = 0`

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

5x² – 4x + 1 = 0

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

5x(x – 2) + 6 = 0

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

`12x^2 - 4sqrt(15)x + 5 = 0`

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

x² – x + 2 = 0

If a and b are distinct real numbers, show that the quadratic equation 2(a² + b²)x² + 2(a + b)x + 1 = 0 has no real roots.

Show that the roots of the equation x² + px – q² = 0 are real for all real values of p and q.

For what values of k are the roots of the quadratic equation 3x² + 2kx + 27 = 0 real and equal?

For what value of k are the roots of the quadratic equation `kx(x - 2sqrt(5)) + 10 = 0` real and equal?

For what values of p are the roots of the equation 4x² + px + 3 = 0 real and equal?

Find the nonzero value of k for which the roots of the quadratic equation 9x² – 3kx + k = 0 are real and equal.

Find the values of k for which the quadratic equation (3k + 1)x² + 2(k + 1)x + 1 = 0  has real and equal roots. 

Find the value of k for which the equation x² + k(2x + k – 1) + 2 = 0 has real and equal roots.

Find the value of p for which the quadratic equation (2p + 1)x² – (7p + 2)x + (7p – 3) = 0 has real and equal roots.

Find that value of p for which the quadratic equation (p + 1)x² – 6(p + 1)x + 3(p + 9) = 0, p ≠ –1 has equal roots. Hence, find the roots of the equation.

If –5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.

If 3 is a root of the quadratic equation x² – x + k = 0, find the value of p so that the roots of the equation x² + 2kx + (k² + 2k + p) = 0 are equal.

If –4 is a root of the equation x² + 2x + 4p = 0, find the value of k for which the quadratic equation x² + px(1 + 3k) + 7(3 + 2k) = 0 has equal roots.

If the quadratic equation (1 + m²)x² + 2mcx + (c² – a²) = 0 has equal roots, prove that c² = a²(1 + m²).  

If the roots of the equation (c² – ab)x² – 2(a² – bc)x + (b² – ac) = 0 are real are equal, show that either a = 0 or (a³ + b³ + c³) = 3abc.

Find the value of p for which the quadratic equation 2x² + px + 8 = 0 has real roots.

Find the value of α for which the equation (α – 12)x² + 2(α – 12)x + 2 = 0 has equal roots.

Find the value of k for which the roots of 9x² + 8kx + 16 = 0 are real and equal.

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

kx² + 6x + 1 = 0

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

x² – kx + 9 = 0

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

9x² + 3kx + 4 = 0

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

5x² – kx + 1 = 0

If a and b are real and a ≠ b then show that the roots of the equation (a – b)x² + 5(a + b)x – 2(a – b) = 0 are real and unequal.

If the roots of the equation (a² + b²)x² – 2(ac + bd)x + (c² + d²) = 0 are equal, prove that ad = bc.

If ad ≠ bc, then prove that the equation (a² + b²)x² + 2(ac + bd)x + (c² + d²) = 0 has no real roots.

If the roots of the equations ax² + 2bx + c = 0 and `bx^2 - 2sqrt(ac)x + b = 0` are simultaneously real then prove that b² = ac.

If `x = (-1)/2`, is a root of the quadratic equation 3x² + 2kx + 3 = 0, find the value of k.

If one root of the quadratic equation 2x² + 2x + k = 0 is `(-1)/3` then find the value of k.

Show that the quadratic equation x² – 8x + 18 = 0 has no real solution.

For what values of k does the quadratic equation 4x² – 12x – k = 0 has no real roots?

Find the value of k for which the roots of the equation 3x² – 10x + k = 0 are reciprocal of each other.

If one root of the equation 5x² + 13x + k = 0 is the reciprocal of the other root then find the value of k.

Find the values of k for which the quadratic equation 3x² + kx + 3 = 0 has real and equal roots?

For what values of a, the quadratic equation 9x² – 3ax + 1 = 0 has real and equal roots?

Find the value of k for which the equation x² + k(2x + k – 1) + 2 = 0 has real and equal roots.

The sum of a natural number and its square is 156. Find the number.

The sum of a natural number and its positive square root is 132. Find the number.

The sum of two natural number is 28 and their product is 192. Find the numbers. 

The sum of the squares of two consecutive positive integers is 365. Find the integers.

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

The product of two consecutive positive integers is 306. Find the integers.

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

Find two consecutive multiples of 3 whose product is 648.

Find the two consecutive positive odd integers whose product is 483.

Find the two consecutive positive even integers whose product is 288. 

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

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.

The difference of two natural numbers is 3 and the difference of their reciprocals is \[\frac{3}{28}\]. Find the numbers.

The difference of two natural numbers is 5 and the difference of their reciprocals is `5/14`. Find the numbers.

The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples. 

The sum of a natural number and its reciprocal is `65/8`. Find the number.

Divide 57 into two parts whose product is 680. 

Divide 27 into two parts such that the sum of their reciprocals is `3/20`. 

Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.

The sum of the squares of two natural numbers is 100. The square of the smaller number is four and a half times the larger number. Find the numbers.

The difference of the squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

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

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 such that the product of its digits is 14. If 45 is added to the number, the digit interchange their places. Find the number. 

The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is `2 9/10`. Find the fraction. 

The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by `1/15`. Find the fraction.

The sum of a number and its reciprocal is `2 1/30`. Find the number. 

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students. 

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

In a class test, the sum of Kamal’s marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Some students planned a picnic. The total budget for food was ₹ 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by ₹ 20. How many students attended the picnic and how much did each student pay for the food?

If the price of a book is reduced by ₹ 5, a person can buy 4 more books for ₹ 600. Find the original price of the book.

A person on tour has ₹ 10800 for his expenses. If he extends his tour by 4 days, he has to cut down his daily expenses by ₹ 90. Find the original duration of the tour.  

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

A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less. How many pens did he buy?

A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of the article.

One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age. Find their present ages.

A man is `3 1/2` times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son.

The sum of the reciprocals of Meena’s ages (in years) 3 years ago and 5 years hence is `1/3`. Find her present ages.

The sum of the ages of a boy and his brother is 25 years and the product of their ages in years is 126. Find their ages.

The product of Tanvy’s age (in years) 5 years ago and her age is 8 years later is 30. Find her present age.

Two years ago, a man’s age was three times the square of his son’s age. In three years time, his age will be four times his son’s age. Find their present ages.

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. Find the original speed of the train.

A train travels at a certain average speed for a distanced of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original 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 its usual speed.

The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speeds of the two train differ by 20 km/hr.

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream. 

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.

Two taps running together can fill a tank in `3 1/13` hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to 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 water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time which each tap can separately fill the tank.

The length of a rectangle is twice its breadth and its area is 288 cm². Find the dimensions of the rectangle.

The length of a rectangular field is three times its breadth. If the area of the field be 147 sq meters, find the length of the field.

The length of a hall is 3 meters more than its breadth. If the area of the hall is 238 sq meters, calculate its length and breadth. 

The perimeter of a rectangular plot is 60 m and its area is 200 sq metres. Find the dimensions of the plot.

A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m². Find the width of the path.

The sum of the areas of two squares is 640 m². If the difference in their perimeter be 64 m, find the sides of the two squares.

The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.

A farmer prepares rectangular vegetable garden of area 180 sq meters. With 39 meters of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden. 

The area of a right-angled triangle is 600 cm². If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.

The area of a right-angled triangle is 96 sq meters. If the base is three times the altitude, find the base.

The area of a right-angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters.

The hypotenuse of a right-angled triangle is 20 meters. If the difference between the lengths of the other sides be 4 meters, find the other sides. 

The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle. 

The hypotenuse of a right-angled triangle is 1 meter less than twice the shortest side. If the third side 1 meter more than the shortest side, find the side, find the sides of the triangle.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 kmph less than that of the faster train, find the speeds of two trains.

A motorboat whose speed is 18 kmph in still water takes 1 hr 30 min more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.

Two pipes together can fill a tank in 12 hours. If the first pipe can fill the tank 10 hours faster than the second then how many hours will the second pipe take to fill the tank?

Two water taps together can fill a tank in `1 7/8` hours. The tap with a longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

In a flight of 600 km, an aircraft was slowed down due to bad weather. The average speed of the trip was reduced by 200 kmph and the time of flight increased by 30 minutes. Find the duration of the flight.

It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool?

Which of the following is a quadratic equation?

Which of the following is a quadratic equation?

Which of the following is not a quadratic equation?

If x = 3 is a solution of the equation 3x² + (k – 1)x + 9 = 0 then k = ?

If one root of the equation 2x² + ax + 6 = 0 is 2 then a = ?

The sum of the roots of the equation x² – 6x + 2 = 0 is ______.

If the product of the roots of the equation x² – 3x + k = 10 is –2 then the value of k is ______.

The ratio of the sum and product of the roots of the equation 7x² – 12x + 18 = 0 is ______.

If one root of the equation 3x² – 10x + 3 = 0 is `1/3` then the other root is ______.

If one root of 5x² + 13x + k = 0 be the reciprocal of the other root then the value of k is ______.

If the sum of the roots of the equation kx² + 2x + 3k = 0 is equal to their product then the value of k is ______.

The roots of a quadratic equation are 5 and –2. Then, the equation is ______.

If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is ______.

If α and β are the roots of the equation 3x² + 8x + 2 = 0 then `(1/α + 1/β)` = ?

The roots of the equation ax² + bx + c = 0 will be reciprocal of each other if 

If the roots of the equation ax² + bx + c = 0 are equal then c = ?

If the equation 9x² + 6kx + 4 = 0 has equal roots then k = ?

If the equation x² + 2(k + 2)x + 9k = 0 has equal roots then k = ?

If the equation 4x² – 3kx + 1 = 0 has equal roots then k = ?

The roots of ax² + bx + c = 0, a ≠ 0 are real and unequal, if (b² – 4ac) is ______.

In the equation ax² + bx + c = 0, it is given that D = (b² – 4ac) > 0. Then, the roots of the equation are ______.

The roots of the equation 2x² – 6x + 7 = 0 are ______.

The roots of the equation 2x² – 6x + 3 = 0 are ______.

If the roots of 5x² – kx + 1 = 0 are real and distinct then

If the equation x² + 5kx + 16 = 0 has no real roots then

If the equation x² – kx + 1 = 0 has no real roots then

For what value of k, the equation kx² – 6x – 2 = 0 has real roots?

The sum of a number and its reciprocal is `2 1/20`. The number is ______.

The perimeter of a rectangle is 82 m and its area is 400 m². The breadth of the rectangle is ______.

The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m². The breadth of the field is ______.

The roots of the quadratic equation 2x² – x – 6 = 0 are ______.

The sum of two natural numbers is 8 and their product is 15., Find the numbers. 

Show that x = –3 is a solution of x² + 6x + 9 = 0.

Show that x = –2 is a solution of 3x² + 13x + 14 = 0.

If `x = (-1)/2` is a solution of the quadratic equation 3x² + 2kx – 3 = 0, find the value of k.

Find the roots of the quadratic equation 2x² – x – 6 = 0.

Find the solution of the quadratic equation `3sqrt(3)x^2 + 10x + sqrt(3) = 0`.

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal then find the value of k.

If the quadratic equation `px^2 - 2sqrt(5)px + 15 = 0` has two equal roots then find the value of p.

If 1 is a root of the equation ay² + ay + 3 = 0 and y² + y + b = 0 then find the value of ab.

If one zero of the polynomial `x^2 - 4x + 1` is `(2 + sqrt(3))`, write the other zero.

If one root of the quadratic equation 3x² – 10x + k = 0 is reciprocal of the other, find the value of k.

If the roots of the quadratic equation px(x – 2) + 6 = 0 are equal, find the value of p.

Find the value of k so that the quadratic equation x² – 4kx + k = 0 has equal roots.

Find the value of k for which the quadratic equation 9x² – 3kx + k = 0 has equal roots.

Solve: `x^2 - (sqrt(3) + 1)x + sqrt(3) = 0`.

Solve: 2x² + ax – a² = 0.

Solve: `3x^2 + 5sqrt(5)x - 10 = 0`.

Solve: `sqrt(3)x^2 + 10x - 8sqrt(3) = 0`.

Solve: `sqrt(3)x^2 - 2sqrt(2)x - 2sqrt(3) = 0`.

Solve: `4sqrt(3)x^2 + 5x - 2sqrt(3) = 0`.

Solve: 4x² + 4bx – (a² – b²) = 0. 

Solve: x² + 5x – (a² + a – 6) = 0.

Solve: x² + 6x – (a² + 2a – 8) = 0.

Solve: x² – 4ax + 4a² – b² = 0.