#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

#### Selina Selina ICSE Concise Mathematics Class 10

## Chapter 5 : Quadratic Equations

#### Page 0

Solve each of the following equations by factorization:

`X^2 – 10x – 24 = 0 `

Solve `2x^2 - 1/2 x = 0`

Solve each of the following equations by factorization:

x(x – 5) = 24

Solve each of the following equations by factorization:

`9/2x=5+x^2`

Solve each of the following equations by factorization :

`6/x=1+x`

Solve each of the following equations by factorization:

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

Solve each of the following equations by factorization:

`x+1/x=2.5`

Solve the following quadratic equations by factorization:

`(2x – 3)^2 = 49`

Solve the following quadratic equations by factorization:

`2(x^2 – 6) = 3 ( x – 4)`

Solve the following quadratic equations by factorization:

(x + 1) (2x + 8) = (x+7) (x+3)

Solve the following quadratic equations by factorization:

`x^2 – (a + b) x + ab = 0`

Solve the following quadratic equations by factorization:

`(x + 3)^2 – 4(x + 3) – 5 = 0 `

Solve the following quadratic equations by factorization:

`4(2x – 3)^2 – (2x – 3) – 14 = 0`

Solve the following quadratic equations by factorization:

`(3x-2)/(2x-3)=(3x-8)/(x+4)`

Solve the following quadratic equations by factorization:

`100/x-100/(x+5)=1`

Solve the following quadratic equations by factorization:

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

Solve the following quadratic equations by factorization:

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

Solve the following quadratic equations by factorization:

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

Solve the following quadratic equations by factorization:

`(1+1/(x+1)) (1-1/(x-1))=7/8`

Find the quadratic equation, whose solution set is:

{3,5}

Find the quadratic equation, whose solution set is:

{−2, 3}

Find the quadratic equation, whose solution set is:

{5, −4,}

Find the quadratic equation, whose solution set is:

`{−3, (−2)/5}`

Find the value of x, if a+1=0 and `x^2 + ax – 6 = 0`

Find the value of x, if a + 1 = 0 and x2 + ax – 6 = 0

Use the substitution y = 2x + 3 to solve for x, if` 4 (2x + 3)^2 − (2x + 3) − 14 = 0 `

Without solving the quadratic equation 6x^{2} – x – 2=0, find whether x = 2/3 is a solution of this equation or not.

Determine whether x = − 1 is a root of the equation `x^2 − 3x + 2 = 0 `or not.

If x = 2/3 is a solution of the quadratic equation 7x^{2}+mx – 3=0; Find the value of m.

If x = − 3 and` x = 2/3 `are solution of quadratic equation `mx^2 + 7x + n = 0`, find the values of m and n.

If quadratic equation `x^2 – (m + 1) x + 6 = 0 `has one root as x = 3; find the value of m and the other root of the equation.

#### Page 0

Solve the following equation using the formula

`x^2 - 6x = 27`

Solve the following equation using the formula

`x^2 + 10x + 21 = 0`

Solve each of the following equations using the formula:

`x^2 + 6x – 10 = 0`

Solve each of the following equations using the formula:

`x^2 + 2x – 6 = 0`

Solve each of the following equations using the formula:

`3x^2 + 2x – 1 = 0`

Solve the following equations using the formula

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

Solve each of the following equations using the formula:

`2/3x=-1/6x^2-1/3`

Solve each of the following equations using the formula:

`1/15x^2+5/3=2/3x`

Solve each of the following equations using the formula:

`x^2-6=2sqrt2x`

Solve each of the following equations using the formula:

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

Solve each of the following equations using the formula :

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

Solve each of the following equations using the formula:

`sqrt6x^2-4x-2sqrt6=0`

Solve each of the following equations using the formula:

`(2x)/(x-4)+(2x-5)/(x-3)=8 1/3`

Solve each of the following equations using the formula:

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

Without solving comment upon the nature of roots of each of the following equations:

7x2 – 9x + 2 = 0

Without solving comment upon the nature of roots of each of the following equations:

6x2 – 13x + 4 = 0

Without solving comment upon the nature of roots of each of the following equations:

`25x^2 − 10x + 1 = 0 `

Without solving comment upon the nature of roots of each of the following equations:

`x^2 – ax – b^2 = 0`

Without solving comment upon the nature of roots of each of the following equations :

`x^2+2sqrt3x-9=0`

Without solving comment upon the nature of roots of each of the following equations:

`2x^2 + 8x + 9 = 0`

Find the value of p, if the following quadratic equation has equal roots: 4x^{2} – (p – 2)x + 1 = 0

The equation` 3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.

Find the value of m, if the following equation has equal roots : (m – 2)x^{2} – (5+m)x +16 =0

#### Page 0

Solve the following equations for x and give, in each case, your answer correct to one decimal place :

x^{2} – 8x+5=0

Solve the following equations for x and give, in given case, your answer correct to one decimal place :

5x^{2} +10x – 3 =0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

2x^{2} – 10x +5=0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

4x + 6/x + 13 = 0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

x^{2} – 3x – 9 =0

Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :

`x^2 - 5x - 10 = 0`

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

3x^{2} – 12x – 1 =0

Solve the following equations for x and give, in each case, your answer correct to two decimal places :

`x^2 - 16x + 6 = 0`

Solve the following equations for x and give, in each case, your answer correct to 3 decimal places

2x^{2} + 11x + 4= 0

Solve x^{4} – 10x^{2} +9 =0

Solve:

x^{4} – 2x^{2} – 3 =0

Solve : (x^{2} – x)^{2} + 5(x^{2} – x)+ 4=0

Solve (x^{2} – 3x)^{2} – 16(x^{2} – 3x) – 36 =0

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

Solve `((2x - 3)/(x -1)) - 4((x - 1)/(2x - 3)) = 3`

Solve `((3x + 1)/(x + 1)) + ((x + 1)/(3x + 1)) = 5/2`

`3sqrt(x/5)+3sqrt(5/x)=10`

Solve the equation `2x - 1/x = 7`.Write your answer correct to two decimal places.

Solve the following equation and give your answer correct to 3 significant figures: 5x² – 3x – 4 = 0

Solve for x using the quadratic formula. Write your answer correct to two significant figures.

(x – 1)^{2} – 3x + 4 = 0

#### Page 0

Solve `(2x)/(x - 3) + 1/(2x + 3) + (3x + 9)/(x - 3)(2x +3) = 0; x != 3, x != - 3/2`

Solve: (2x+3)^{2 }= 81

Solve `a^2x^2 - b^2 = 0`

Solve `x^2 - 11/4 x + 15/8 = 0`

Solve `x + 4/x = -4; x != 0`

Solve: 2x^{4} – 5x² + 3 = 0

**The age of the father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.**

Solve: x^{4} – 2x² – 3 = 0.

Solve `9(x^2 + 1/x^2) - 9(x - 1/x) - 52 = 0`

Solve `2(x^2 + 1/x^2) - (x + 1/x) = 11`

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

Solve : (x² + 5x + 4)(x² + 5x + 6) = 120

`x^2 - 5x - 10 = 0`

Solve of the following equations, giving answer upto two decimal places.

3x^{2} – x – 7 =0

Solve `(x/(x + 2))^2 - 7(x/(x + 2)) + 12 = 0; x != -2`

Solve : x^{2} – 11x – 12 =0; when x ∈ N

Solve x^{2} – 4x – 12 =0; when x ∈ I

Solve 2x^{2} – 9x + 10 =0; when x ∈ Q

Solve : (a + b)²x² – (a + b)x – 6 = 0; a + b ≠ 0

Solve `1/p + 1/q + 1/x = 1/(x + p + q)`

Solve x(x + 1) + (x + 2)(x + 3) = 42

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

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`(m - 3)x^2 - 4x + 1 = 0`

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`3x^2 + 12x + (m + 7) = 0`

For each equation given below find the values of m so that the equation has equal roots. Also find the solution of equation

`x^2 - (m + 2)x + (m + 5) = 0`

Without solving the following quadratic equation Find the value of p for which the roots are equal

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

Without solving the following quadratic equation, find the value of m for which the given equation has equation has real and equal roots.

`x^2 + 2(m - 1)x + (m + 5) = 0`

#### Selina Selina ICSE Concise Mathematics Class 10

#### Textbook solutions for Class 10

## Selina solutions for Class 10 Mathematics chapter 5 - Quadratic Equations

Selina solutions for Class 10 Maths chapter 5 (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 CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 5 Quadratic Equations are Nature of Roots, Quadratic Equations, Solutions of Quadratic Equations by Factorization.

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