CBSE Class 10 Mathematics Quadratic Equations MCQs Set 29

Practice MCQs for Class 10 Mathematics Chapter 04 Quadratic Equations

Explore reliable objective questions for Chapter 04 Quadratic Equations tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Access Chapter 04 Quadratic Equations Questions and Solutions

Access the complete set of multiple-choice questions for Chapter 04 Quadratic Equations below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: The value of 5x² − 7x + 2 at x = 3 is
(a) 20
(b) 26
(c) 32
(d) 14
Show Answer & Explanation

Answer: (b) 26

Explanation:
1. 5(9) − 7(3) + 2 = 45 − 21 + 2 = 26.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 2: The value of 3y + 8 − 2y² at y = −3 is
(a) 19
(b) −1
(c) −27
(d) −19
Show Answer & Explanation

Answer: (d) −19

Explanation:
1. 3(−3) + 8 − 2(9) = −9 + 8 − 18 = −19.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 3: The value of √2 x² + 3x + 1 at x = √2 is
(a) 3√2 + 1
(b) 2√2 + 1
(c) 5√2 + 1
(d) 5√2 − 1
Show Answer & Explanation

Answer: (c) 5√2 + 1

Explanation:
1. √2(2) + 3√2 + 1 = 2√2 + 3√2 + 1 = 5√2 + 1.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 4: If x = −2 is a zero of the quadratic polynomial 4x² − 3mx + 5, then m equals
(a) 7/2
(b) −3/2
(c) 2
(d) −7/2
Show Answer & Explanation

Answer: (d) −7/2

Explanation:
1. Put x = −2: 4(4) − 3m(−2) + 5 = 21 + 6m = 0, so m = −7/2.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 5: Which of the following is a quadratic equation?
(a) 8x³ − 3x = 0
(b) 8x − 15 = 0
(c) x(x + 2) = x² − 5
(d) 15x² + 27x − 33 = 0
Show Answer & Explanation

Answer: (d) 15x² + 27x − 33 = 0

Explanation:
1. 15x² + 27x − 33 = 0 has degree 2. 8x³ − 3x is cubic, 8x − 15 is linear and x(x + 2) = x² − 5 simplifies to 2x + 5 = 0, which is linear.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 6: Determine which of x = −2/√3 and x = −3√3 are solutions of √3x² + 11x + 6√3 = 0.
(a) only x = −2/√3
(b) both of them
(c) only x = −3√3
(d) neither of them
Show Answer & Explanation

Answer: (b) both of them

Explanation:
1. For x = −2/√3: √3(4/3) − 22/√3 + 6√3 = 4/√3 − 22/√3 + 18/√3 = 0. For x = −3√3: √3(27) − 33√3 + 6√3 = 0. Both satisfy the equation.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 7: The value of m for which x = 2 is a solution of 3x² + 2mx − 3 = 0 is
(a) −9/4
(b) 9/4
(c) −3/4
(d) −3
Show Answer & Explanation

Answer: (a) −9/4

Explanation:
1. Put x = 2: 12 + 4m − 3 = 0, so 4m = −9 and m = −9/4.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 8: If x + a = 0 is a solution of x² + 2ax − m = 0, then m equals
(a) −a²
(b) a²
(c) 3a²
(d) −2a²
Show Answer & Explanation

Answer: (a) −a²

Explanation:
1. x = −a gives a² − 2a² − m = 0, so m = −a².

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 9: Find the roots of the equation x² + 5x + 6 = 0.
(a) 3 and 2
(b) −3 and 2
(c) −1/3 and −1/2
(d) −3 and −2
Show Answer & Explanation

Answer: (d) −3 and −2

Explanation:
1. Factorising, x² + 5x + 6 = (x + 2)(x + 3) = 0, so the roots are −3 and −2.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 10: Find the roots of the equation x² − 8x − 33 = 0.
(a) −3 and 11
(b) 3 and −11
(c) −3 and −11
(d) −1/3 and 1/11
Show Answer & Explanation

Answer: (a) −3 and 11

Explanation:
1. Factorising, x² − 8x − 33 = (x − 11)(x + 3) = 0, so the roots are −3 and 11.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 11: Find the roots of the equation x² + 5x − 6 = 0.
(a) 6 and −1
(b) −6 and 1
(c) −6 and −1
(d) −1/6 and 1
Show Answer & Explanation

Answer: (b) −6 and 1

Explanation:
1. Factorising, x² + 5x − 6 = (x − 1)(x + 6) = 0, so the roots are −6 and 1.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 12: Find the roots of the equation x² − 5x − 6 = 0.
(a) 1 and −6
(b) −1 and 6
(c) −1 and −6
(d) −1 and 1/6
Show Answer & Explanation

Answer: (b) −1 and 6

Explanation:
1. Factorising, x² − 5x − 6 = (x − 6)(x + 1) = 0, so the roots are −1 and 6.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 13: Find the roots of the equation 4x² − 25x − 21 = 0.
(a) 3/4 and −7
(b) −3/4 and −7
(c) −4/3 and 1/7
(d) −3/4 and 7
Show Answer & Explanation

Answer: (d) −3/4 and 7

Explanation:
1. Factorising, 4x² − 25x − 21 = (x − 7)(4x + 3) = 0, so the roots are −3/4 and 7.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 14: Find the roots of the equation 10x² − 7x − 12 = 0.
(a) 4/5 and −3/2
(b) −4/5 and −3/2
(c) −5/4 and 2/3
(d) −4/5 and 3/2
Show Answer & Explanation

Answer: (d) −4/5 and 3/2

Explanation:
1. Factorising, 10x² − 7x − 12 = (2x − 3)(5x + 4) = 0, so the roots are −4/5 and 3/2.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 15: Find the roots of the equation 3x² − 7x − 6 = 0.
(a) −2/3 and 3
(b) 2/3 and −3
(c) −2/3 and −3
(d) −3/2 and 1/3
Show Answer & Explanation

Answer: (a) −2/3 and 3

Explanation:
1. Factorising, 3x² − 7x − 6 = (x − 3)(3x + 2) = 0, so the roots are −2/3 and 3.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 16: Find the roots of the equation x(4x − 7) = 0.
(a) 0 and −7/4
(b) 2 and 4/7
(c) 0 and 7/4
(d) 1 and 3/4
Show Answer & Explanation

Answer: (c) 0 and 7/4

Explanation:
1. Factorising, x(4x − 7) = x(4x − 7) = 0, so the roots are 0 and 7/4.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 17: Find the roots of x(x + 1) + (x + 2)(x + 3) = 26.
(a) 2 and −5
(b) −2 and 5
(c) 2 and 5
(d) −2 and −5
Show Answer & Explanation

Answer: (a) 2 and −5

Explanation:
1. Expanding: x² + x + x² + 5x + 6 = 26, so 2x² + 6x − 20 = 0, i.e. x² + 3x − 10 = 0 = (x + 5)(x − 2). The roots are 2 and −5.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 18: Find the roots of x(x − 1) + (x − 2)(x − 3) = 42.
(a) −6 and 3
(b) 6 and 3
(c) 6 and −3
(d) −6 and −3
Show Answer & Explanation

Answer: (c) 6 and −3

Explanation:
1. Expanding: x² − x + x² − 5x + 6 = 42, so 2x² − 6x − 36 = 0, i.e. x² − 3x − 18 = 0 = (x − 6)(x + 3). The roots are 6 and −3.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 19: The nature of the roots of 2x² − 5x + 5 = 0 is
(a) two distinct real roots
(b) no real roots
(c) two equal real roots
(d) one real root
Show Answer & Explanation

Answer: (b) no real roots

Explanation:
1. D = b² − 4ac = -5² − 4(2)(5) = -15, so the equation has no real roots.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 20: The nature of the roots of 4x² − 4x + 1 = 0 is
(a) two equal real roots
(b) two distinct real roots
(c) no real roots
(d) one real and one imaginary root
Show Answer & Explanation

Answer: (a) two equal real roots

Explanation:
1. D = b² − 4ac = -4² − 4(4)(1) = 0, so the equation has two equal real roots.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 21: The nature of the roots of 5x² − 8x + 2 = 0 is
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) two equal real roots and D < 0
Show Answer & Explanation

Answer: (a) two distinct real roots

Explanation:
1. D = b² − 4ac = -8² − 4(5)(2) = 24, so the equation has two distinct real roots.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 22: The nature of the roots of 6x² − 5x − 6 = 0 is
(a) two equal real roots
(b) no real roots
(c) two equal real roots and D < 0
(d) two distinct real roots
Show Answer & Explanation

Answer: (d) two distinct real roots

Explanation:
1. D = b² − 4ac = -5² − 4(6)(-6) = 169, so the equation has two distinct real roots.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 23: The discriminant of 2x² + 3x − 2 = 0 is
(a) 29
(b) −25
(c) 25
(d) 50
Show Answer & Explanation

Answer: (c) 25

Explanation:
1. D = b² − 4ac = 25.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 24: The discriminant of x² − x + 1 = 0 is
(a) 1
(b) 3
(c) −6
(d) −3
Show Answer & Explanation

Answer: (d) −3

Explanation:
1. D = b² − 4ac = -3.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

Question 25: The roots of x² − 2√2x − 6 = 0 are
(a) −3√2 and √2
(b) 3√2 and −√2
(c) √2 and 3√2
(d) 2√2 and −3√2
Show Answer & Explanation

Answer: (b) 3√2 and −√2

Explanation:
1. D = (2√2)² + 24 = 32. x = (2√2 ± 4√2)/2 = 3√2 or −√2.

Teacher's Note:
1. Bring the equation to the form ax² + bx + c = 0 first, then factorise or use the discriminant D = b² − 4ac.
2. Always check the roots by substitution.

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Practice MCQs for Class 10 Mathematics Chapter 04 Quadratic Equations

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