ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations Overview

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations PDF

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations PDF

ICSE Class 10 Maths Selina Solutions Chapter 5 Exercise 5(A) Page No: 54

1. Find which of the following equations are quadratic:

(i) (3x – 1) ² = 5(x + 8)

(ii) 5x ² – 8x = -3(7 – 2x)

(iii) (x -4) (3x + 1) = (3x – 1) (x + 2)

(iv) x ² + 5x – 5 = (x – 3) ²

(v) 7x ³ – 2x ² + 10 = (2x – 5) ²

(vi) (x – 1) ² + (x + 2) ² + 3(x + 1) = 0

Solution:

2. (i) Is x = 5 a solution of the quadratic equation x ² – 2x – 15 = 0?

Solution:

(ii) Is x = -3 a solution of the quadratic equation 2x ² – 7x + 9 = 0?

Solution:

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations Exercise 5(B) Page No: 56

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

(i) 7x ² – 9x +2 = 0 (ii) 6x ² – 13x +4 = 0

(iii) 25x ² – 10x + 1= 0 (iv) x ² + 2√3x – 9 = 0

(v) x ² – ax – b ² = 0 (vi) 2x ² + 8x + 9 = 0

Solution:

2. Find the value of ‘p’, if the following quadratic equations has equal roots:

(i) 4x ² – (p – 2)x + 1 = 0

(ii) x ² + (p – 3)x + p = 0

Solution:

ICSE Class 10 Maths Selina Solutions Chapter 5 Exercise 5(C) Page No: 59

Solve equations, number 1 to 20, given below, using factorization method:

1. x ² – 10x – 24 = 0

Solution:

2. x ² – 16 = 0

Solution:

3. 2x ² – ½ x = 0

Solution:

4. x(x – 5) = 24

Solution:

5. 9/2 x = 5 + x ²

Solution:

6. 6/x = 1 + x

Solution:

7. x = (3x + 1)/ 4x

Solution:

8. x + 1/x = 2.5

Solution:

9. (2x – 3) ² = 49

Solution:

10. 2(x ² – 6) = 3(x – 4)

Solution:

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

Solution:

12. x ² – (a + b)x + ab = 0

Solution:

13. (x + 3) ² – 4(x + 3) – 5 = 0

Solution:

14. 4(2x – 3) ² – (2x – 3) – 14 = 0

Solution:

15. 3x – 2/ 2x- 3 = 3x – 8/ x + 4

Solution:

16. 2x ² – 9x + 10 = 0, when:

(i) x ∈ N (ii) x ∈ Q

Solution:

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations Exercise 5(D) Page No: 59

1. Solve, each of the following equations, using the formula:

(i) x ² – 6x = 27

Solution:

(ii) x ² – 10x + 21 = 0

Solution:

(iii) x ² + 6x – 10 = 0

Solution:

(iv) x ² + 2x – 6 = 0

Solution:

(v) 3x ² + 2x – 1 = 0

Solution:

(vi) 2x ² + 7x + 5 = 0

Solution:

(vii) 2/3 x = -1/6 x ² – 1/3

Solution:

(viii) 1/15 x ² + 5/3 = 2/3 x

Solution:

(ix) x ² – 6 = 2 √2 x

Solution:

(x) 4/x – 3 = 5/ (2x + 3)

Solution:

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

Solution:

(xii) √6x ² – 4x – 2√6 = 0

Solution:

(xiii) 2x/ x – 4 + (2x – 5)/(x – 3) =

Solution:

(xiv)

Solution:

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

(i) x ² – 8x +5 = 0

(ii) 5x ² + 10x – 3 = 0

Solution:

3. Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places:

(i) 2x ² – 10x + 5 = 0

Solution:

(ii) 4x + 6/x + 13 = 0

Solution:

(iii) 4x ² – 5x – 3 = 0

Solution:

(iv) x ² – 3x – 9 = 0

Solution:

(v) x ² – 5x – 10 = 0

Solution:

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

(i) 3x ² – 12x – 1 = 0

(ii) x ² – 16 x +6 = 0

(iii) 2x ² + 11x + 4 = 0

Solution:

5. Solve:

(i) x ⁴ – 2x ² – 3 = 0

Solution:

(ii) x ⁴ – 10x ² + 9 = 0

Solution:

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations Exercise 5(E) Page No: 66

1. Solve each of the following equations:

Solution:

2. (2x + 3) ² = 81

Solution:

3. a ² x ² – b ² = 0

Solution:

4. x ² – 11/4 x + 15/8 = 0

Solution:

5. x + 4/x = -4; x ≠ 0

Solution:

6. 2x ⁴ – 5x ² + 3 = 0

Solution:

7. x ⁴ – 2x ² – 3 = 0

Solution:

8.

Solution:

9.

Solution:

10.

Solution:

ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations Exercise 5(F) Page No: 67

1. Solve:

(i) (x + 5) (x – 5) = 24

Solution:

(ii) 3x ² – 2√6x + 2 = 0

Solution:

(iii) 3√2x ² – 5x – √2 = 0

Solution:

(iv) 2x – 3 = √(2x ² – 2x + 21)

Solution:

2. One root of the quadratic equation 8x ² + mx + 15 = 0 is ¾. Find the value of m. Also, find the other root of the equation.

Solution:

3. Show that one root of the quadratic equation x ² + (3 – 2a)x – 6a = 0 is -3. Hence, find its other root.

Solution:

4. If p – 15 = 0 and 2x ² + px + 25 = 0: find the values of x.

Solution:

5. Find the solution of the quadratic equation 2x ² – mx – 25n = 0; if m + 5 = 0 and n – 1 = 0.

Solution:

6. If m and n are roots of the equation: 1/x – 1/(x-2) = 3: where x ≠ 0 and x ≠ 2; find m x n.

Solution:

Last Minute Tips for ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations

With the ICSE Class 10 board exams having started from 17 February 2026, smart and focused revision is the key to scoring well. Quadratic Equations is an important and high-weightage chapter, so clarity in methods and formulas is essential.

• Revise all three methods – factorisation, completing the square, and quadratic formula.

• Memorise the quadratic formula correctly and practice substituting values carefully.

• Check the discriminant (D = b² – 4ac) to identify the nature of roots.

• Practice 3–4 important sums to improve speed and accuracy.

• Avoid calculation mistakes by solving step-by-step and rechecking signs.