CBSE Class 10 Mathematics Quadratic Equations MCQs Set 30

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Chapter 04 Quadratic Equations

Access targeted multiple-choice questions for Chapter 04 Quadratic Equations designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Chapter 04 Quadratic Equations MCQs for Class 10 Mathematics

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 roots of 16x² − 1 = 0 are
(a) 4 and −4
(b) 1/4 and −1/4
(c) 1/16 and −1/16
(d) 1/4 only
Show Answer & Explanation

Answer: (b) 1/4 and −1/4

Explanation:
1. x² = 1/16, so x = ±1/4.

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 2: The roots of 4x² − 7x + 3 = 0 are
(a) −1 and −3/4
(b) 4/3 and 1
(c) 3 and 4
(d) 1 and 3/4
Show Answer & Explanation

Answer: (d) 1 and 3/4

Explanation:
1. D = 49 − 48 = 1. x = (7 ± 1)/8 = 1 or 3/4.

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 3: The roots of x² = 3x are
(a) 3 only
(b) 0 and 3
(c) 0 and −3
(d) −3 and 3
Show Answer & Explanation

Answer: (b) 0 and 3

Explanation:
1. x² − 3x = x(x − 3) = 0. The roots are 0 and 3. (Dividing by x would lose the root x = 0.)

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: The values of p for which 2x² + 3x + p = 0 has real roots are
(a) p ≥ 9/8
(b) p ≤ 9/8
(c) p < 9/8
(d) p ≤ 8/9
Show Answer & Explanation

Answer: (b) p ≤ 9/8

Explanation:
1. Real roots need D = 9 − 8p ≥ 0, so p ≤ 9/8.

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: The quadratic equation 3x² − 2px − 5 = 0 has real roots for
(a) p > 0 only
(b) all real values of p
(c) p ≥ 0 only
(d) no value of p
Show Answer & Explanation

Answer: (b) all real values of p

Explanation:
1. D = 4p² + 60 > 0 for every real p, so the roots are always real and distinct.

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: The real roots of 4x² + x − 3 = 0 are
(a) −1 and 3/4
(b) 1 and −3/4
(c) 0 and 7/4
(d) no real roots
Show Answer & Explanation

Answer: (a) −1 and 3/4

Explanation:
1. D = 49 ≥ 0, so real roots exist. Solving gives −1 and 3/4.

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 7: The real roots of 9x² + 30x + 25 = 0 are
(a) 5/3
(b) −10/3
(c) no real roots
(d) −5/3
Show Answer & Explanation

Answer: (d) −5/3

Explanation:
1. D = 0 ≥ 0, so real roots exist. Solving gives −5/3.

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 8: The real roots of 3x² − 3x − 1 = 0 are
(a) −1/2 + √21/6 and −√21/6 − 1/2
(b) 1/2 − √21/6 and 1/2 + √21/6
(c) 3/2 − √21/6 and √21/6 + 3/2
(d) no real roots
Show Answer & Explanation

Answer: (b) 1/2 − √21/6 and 1/2 + √21/6

Explanation:
1. D = 21 ≥ 0, so real roots exist. Solving gives 1/2 − √21/6 and 1/2 + √21/6.

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 9: The quadratic equation whose roots are 5 and −5 is
(a) x² + 25 = 0
(b) x² − 10x + 25 = 0
(c) x² − 25 = 0
(d) x² + 10x − 25 = 0
Show Answer & Explanation

Answer: (c) x² − 25 = 0

Explanation:
1. Sum = 0 and product = −25, so x² − 0x − 25 = x² − 25 = 0.

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: The quadratic equation whose roots are −8 and −3 is
(a) x² − 11x + 24 = 0
(b) x² + 11x − 24 = 0
(c) x² + 5x + 24 = 0
(d) x² + 11x + 24 = 0
Show Answer & Explanation

Answer: (d) x² + 11x + 24 = 0

Explanation:
1. Sum = −11 and product = 24, so x² + 11x + 24 = 0.

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: The quadratic equation whose roots are 1 + √2 and 1 − √2 is
(a) x² + 2x − 1 = 0
(b) x² − 2x + 1 = 0
(c) x² − 2x − 1 = 0
(d) x² − 2x − 3 = 0
Show Answer & Explanation

Answer: (c) x² − 2x − 1 = 0

Explanation:
1. Sum = 2 and product = 1 − 2 = −1, so x² − 2x − 1 = 0.

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: The quadratic equation whose roots are 7 + √7 and 7 − √7 is
(a) x² + 14x + 42 = 0
(b) x² − 14x + 56 = 0
(c) x² − 14x − 42 = 0
(d) x² − 14x + 42 = 0
Show Answer & Explanation

Answer: (d) x² − 14x + 42 = 0

Explanation:
1. Sum = 14 and product = 49 − 7 = 42, so x² − 14x + 42 = 0.

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: The quadratic equation whose roots are √3 and 5√3 is
(a) x² + 6√3x + 15 = 0
(b) x² − 6√3x + 45 = 0
(c) x² − 4√3x + 15 = 0
(d) x² − 6√3x + 15 = 0
Show Answer & Explanation

Answer: (d) x² − 6√3x + 15 = 0

Explanation:
1. Sum = √3 + 5√3 = 6√3 and product = √3 × 5√3 = 15, so x² − 6√3x + 15 = 0.

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: For ax² − 3x − b = 0, the sum of the roots is 6 and the product is −8. Then a and b are
(a) a = 2, b = 16
(b) a = −1/2, b = 4
(c) a = 1/2, b = −4
(d) a = 1/2, b = 4
Show Answer & Explanation

Answer: (d) a = 1/2, b = 4

Explanation:
1. Sum = 3/a = 6 gives a = 1/2. Product = −b/a = −8 gives b = 8a = 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 15: One root of 3x² − px − 6 = 0 is 3. Then p and the other root are
(a) p = 7, other root 2/3
(b) p = −7, other root −2/3
(c) p = 3, other root −2
(d) p = 7, other root −2/3
Show Answer & Explanation

Answer: (d) p = 7, other root −2/3

Explanation:
1. Put x = 3: 27 − 3p − 6 = 0, so p = 7. The product of the roots is −6/3 = −2, so the other root is −2/3.

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: If α and β are the roots of 2x² + 5x − 4 = 0, the value of α³ + β³ is
(a) −245/8
(b) 245/8
(c) −125/8
(d) −185/8
Show Answer & Explanation

Answer: (a) −245/8

Explanation:
1. α³ + β³ = (α + β)³ − 3αβ(α + β) = −125/8 − 3(−2)(−5/2) = −125/8 − 15 = −245/8.

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: If α and β are the roots of 2x² + 5x − 4 = 0, the value of α/β + β/α is
(a) −41/8
(b) 41/8
(c) −25/8
(d) −41/4
Show Answer & Explanation

Answer: (a) −41/8

Explanation:
1. α/β + β/α = (α² + β²)/αβ = (41/4)/(−2) = −41/8.

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: If α and β are the roots of x² − 6x + 1 = 0, the value of α² + β² is
(a) 36
(b) 34
(c) 32
(d) 38
Show Answer & Explanation

Answer: (b) 34

Explanation:
1. α + β = 6 and αβ = 1. α² + β² = 36 − 2 = 34.

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: If α and β are the roots of x² − 6x + 1 = 0, the value of α⁴ + β⁴ is
(a) 1156
(b) 34
(c) 1152
(d) 1154
Show Answer & Explanation

Answer: (d) 1154

Explanation:
1. α² + β² = 34, and α²β² = 1. α⁴ + β⁴ = 34² − 2 = 1154.

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: If α and β are the roots of x² − 6x + 1 = 0, the value of α³ + β³ is
(a) 198
(b) 216
(c) 192
(d) 180
Show Answer & Explanation

Answer: (a) 198

Explanation:
1. α³ + β³ = (α + β)³ − 3αβ(α + β) = 216 − 18 = 198.

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 value of p for which 2x² − 7x + p = 0 has equal roots is
(a) 8/49
(b) −49/8
(c) 7/4
(d) 49/8
Show Answer & Explanation

Answer: (d) 49/8

Explanation:
1. D = 49 − 8p = 0 gives p = 49/8.

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 value of p for which 6x² + 12x − p = 0 has equal roots is
(a) −6
(b) 6
(c) −12
(d) 12
Show Answer & Explanation

Answer: (a) −6

Explanation:
1. D = 144 + 24p = 0 gives p = −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 23: The roots of (4 − m)x² + (2m + 4)x + (8m + 1) = 0 are equal for m =
(a) 0 only
(b) 0 or 3
(c) 3 only
(d) −3 or 0
Show Answer & Explanation

Answer: (b) 0 or 3

Explanation:
1. Equal roots need D = (2m + 4)² − 4(4 − m)(8m + 1) = 0. Expanding, D = 36m² − 108m = 36m(m − 3), so m = 0 or m = 3. In both cases 4 − m ≠ 0, so the equation is quadratic.

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 values of p for which 3px² + 18x + p = 0 has equal roots are
(a) p = ±3
(b) p = ±9
(c) p = ±3√3
(d) p = 3√3 only
Show Answer & Explanation

Answer: (c) p = ±3√3

Explanation:
1. D = 324 − 12p² = 0 gives p² = 27, so p = ±3√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 values of p for which 2px² − 20x + (13p − 1) = 0 has equal roots are
(a) p = 2 or p = −25/13
(b) p = 2 only
(c) p = −2 or 25/13
(d) p = 1/2 or −25/13
Show Answer & Explanation

Answer: (a) p = 2 or p = −25/13

Explanation:
1. D = 400 − 8p(13p − 1) = 0 gives 104p² − 8p − 400 = 0, i.e. 13p² − p − 50 = 0 = (p − 2)(13p + 25). So p = 2 or p = −25/13.

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.

Free study material for Mathematics

Chapter 04 Quadratic Equations Objective Questions & Solutions for Class 10 Mathematics

Class 10 Mathematics Chapter 04 Quadratic Equations Objective Test Questions

Test your conceptual understanding of Chapter 04 Quadratic Equations with these targeted multiple-choice questions. Designed in alignment with the latest CBSE curriculum for Class 10 Mathematics, these problem sets build accuracy and prepare students for objective exams.

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FAQs

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