ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations

ICSE Class 10 Maths Selina Solutions Chapter 5: ICSE Class 10 Maths Selina Solutions for Chapter 5, "Quadratic Equations," make it easy to understand and solve 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:

Benefits of ICSE Class 10 Maths Selina Solutions Chapter 5 Quadratic Equations

• Detailed Explanations: Each solution is broken down into clear, step-by-step instructions, making it easy for students to understand how to solve quadratic equations.
• Expert Preparation: The solutions are created by subject experts at Physics Wallah, ensuring accuracy and clarity in problem-solving methods.
• Comprehensive Coverage: The chapter covers various methods to solve quadratic equations, including factoring, completing the square, and using the quadratic formula, providing students with a thorough understanding of the topic.
• Exam Preparation: These solutions help students prepare for exams by showing how to approach and solve different types of quadratic equations which is important for performing well in the ICSE board exams.
• Confidence Building: By following these well-explained solutions, students can build confidence in their ability to handle quadratic equations and apply their knowledge effectively in exams.