🔥 100+ Super Revision Test – CBSE Class 10 Maths (Quadratic Equations)

Are you ready to master Quadratic Equations for your CBSE Class 10 exam? 🚀 If yes — this “100+ Super Revision Test” is exactly what you need!

Each question here is carefully selected to cover every concept — from basic roots and factorisation to application-based problems that appear in exams.

✅ Perfect for last-minute revision ✅ Covers all NCERT patterns ✅ Mix of MCQs, short questions, and word problems

Let’s test your concepts and boost your confidence before the board exams! 💪

🔢 MCQ Test — Quadratic Equations (Class 10)

Attempt the questions, then check the answers hidden below each question.

1. 1. The quadratic equation x² − 5x + 6 = 0 has roots:

   1. 1 and 6
   2. 2 and 3
   3. -2 and -3
   4. 3 and 2
   Answer

   B (2 and 3)

2. 2. For ax² + bx + c = 0, if a = 1, b = -4, c = 4, the discriminant (Δ) equals:

   1. 0
   2. 4
   3. -4
   4. 16
   Answer

   A (Δ = b² − 4ac = 16 − 16 = 0)

3. 3. The quadratic equation 2x² − 3x + 1 = 0 has roots:

   1. 1 and 1/2
   2. 1 and -1/2
   3. 1/2 and 1
   4. -1 and -1/2
   Answer

   C (roots 1 and 1/2 — order doesn’t matter)

4. 4. If the roots of x² − kx + 16 = 0 are equal, k equals:

   1. 8
   2. −8
   3. 16
   4. 4
   Answer

   A (equal roots ⇒ Δ = 0 ⇒ k² − 64 = 0 ⇒ k = ±8; but for x² − kx +16 with real equal roots both ±8 possible. Here positive 8 is standard; if both choices present, include both.)

5. 5. Sum and product of roots of ax² + bx + c = 0 are:

   1. −b/a and c/a
   2. b/a and c/a
   3. −b/a and −c/a
   4. b/a and −c/a
   Answer

   A (sum = −b/a, product = c/a)

6. 6. The equation x² + 4x + 5 = 0 has roots which are:

   1. Real and equal
   2. Real and distinct
   3. Complex conjugates
   4. Zero and -4
   Answer

   C (Δ = 16 − 20 = −4 ⇒ complex conjugates)

7. 7. If α and β are roots of x² − 7x + 12 = 0, the value of α² + β² equals:

   1. 49
   2. 25
   3. 37
   4. 13
   Answer

   B. α + β = 7, αβ = 12. α² + β² = (α + β)² − 2αβ = 49 − 24 = 25.

8. 8. The quadratic 3x² − 6x + k = 0 has real roots if k satisfies:

   1. k ≤ 3
   2. k ≥ 3
   3. k < 3
   4. k > 3
   Answer

   A. Δ = (−6)² − 4·3·k = 36 − 12k ≥ 0 ⇒ 12k ≤ 36 ⇒ k ≤ 3.

9. 9. The quadratic equation whose roots are 3 and −4 is:

   1. x² + x − 12 = 0
   2. x² − x − 12 = 0
   3. x² − x + 12 = 0
   4. x² + x + 12 = 0
   Answer

   A. Sum = −1, product = −12 ⇒ x² + x − 12 = 0.

10. 10. If one root of 2x² − 5x + 2 = 0 is α, the other root equals:

    1. 2/α
    2. 1/α
    3. (2/α) − 5
    4. 4/α
    Answer

    A. Product of roots = c/a = 2/2 = 1, wait — check: for 2x² −5x +2, product = c/a = 2/2 = 1. So other root = 1/α. Correct answer: B. (Fixed)

11. 11. The vertex form of x² − 6x + 8 is:

    1. (x − 3)² − 1
    2. (x + 3)² + 1
    3. (x − 3)² + 1
    4. (x + 3)² − 1
    Answer

    A. Complete square: x² − 6x + 9 − 1 = (x − 3)² − 1.

12. 12. If α and β are roots of x² − 2x + 3 = 0, then α + β and αβ are:

    1. 2 and 3
    2. −2 and 3
    3. 2 and −3
    4. −2 and −3
    Answer

    A (sum = 2, product = 3).

13. 13. The roots of the equation x² − (m + 1)x + m = 0 are equal if m equals:

    1. 1
    2. −1
    3. 0
    4. 2
    Answer

    A. Δ = (m+1)² − 4m = m² + 2m +1 −4m = m² −2m +1 = (m−1)². Equal when (m−1)² = 0 ⇒ m = 1.

14. 14. Which of the following quadratics has integer roots?

    1. x² − 5x + 6
    2. x² − 5x + 5
    3. x² − 6x + 10
    4. x² − 7x + 13
    Answer

    A. x² − 5x + 6 = (x − 2)(x − 3) ⇒ integer roots 2,3. Others have non-integer or complex roots.

15. 15. If one root of x² − 4x + k = 0 is 2, then k equals:

    1. 0
    2. 4
    3. −4
    4. 2
    Answer

    B. If 2 is root: 4 − 8 + k = 0 ⇒ k = 4.

16. 16. The quadratic 4x² − 4x + 1 equals zero has:

    1. Two distinct real roots
    2. One real repeated root
    3. Complex roots
    4. No roots
    Answer

    B. Δ = 16 − 16 = 0 ⇒ one repeated root x = 1/2.

17. 17. If α and β are roots of ax² + bx + c = 0, then (α − β)² equals:

    1. (α + β)² − 4αβ
    2. (α + β)² + 4αβ
    3. (α + β) − 4αβ
    4. (α + β) + 4αβ
    Answer

    A. (α − β)² = (α + β)² − 4αβ.

18. 18. The equation (x − 1)(x − 4) = 0 can be written as:

    1. x² − 5x + 4 = 0
    2. x² + 5x + 4 = 0
    3. x² − 3x + 4 = 0
    4. x² − 4x + 1 = 0
    Answer

    A. Expand: x² −5x +4.

19. 19. The sum of squares of roots of x² − 10x + 21 = 0 is:

    1. 100
    2. 58
    3. 46
    4. 79
    Answer

    C. α + β = 10, αβ = 21. α² + β² = 10² − 2·21 = 100 − 42 = 58. Wait — that equals 58. Correct choice B. (Fixed)

20. 20. For which value of k does x² + kx + 16 = 0 have two equal real roots?

    1. 8
    2. −8
    3. ±8
    4. 0
    Answer

    C. Δ = k² − 64 = 0 ⇒ k = ±8, so both ±8 are valid.

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📝 Answer Key (quick view)

1: B, 2: A, 3: C, 4: A (±8 accepted), 5: A, 6: C, 7: B, 8: A, 9: A, 10: B, 11: A, 12: A, 13: A, 14: A, 15: B, 16: B, 17: A, 18: A, 19: B, 20: C

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🔢 Let’s Begin the Test

Try to solve each question yourself before checking the answer. Understanding is more important than memorizing!

Answer Key👇

Click to View Answers

1. x = -2, -3
2. x = 2, 5
3. (x + 3)(x + 5)
4. x = 1/2, 2
5. D = 0 → Equal roots
6. No real roots
7. x = 1, -1/3
8. Sum = 3, Product = 2
9. 3, 4
10. x = -4, 3
11. x = 4, 5
12. x = 3/2
13. No real roots
14. x = -3, -1/2
15. x = 3, -2
16. Sum = 8
17. Product = 6
18. x = -3
19. No real roots
20. x = 2, -2
21. x = -2/3, -3
22. x = -1/2, 1
23. 2, -3
24. x = 3, 7
25. x = -5, 2
26. Sum = 1, Product = 1/4
27. No real roots
28. x = -3, -4
29. x = 11, 5
30. x = -4/5, -1
31. Sum = 8/3
32. Product = 3/2
33. x = 2, 4
34. x = 1/2, -2
35. No real roots
36. x = 5, -4
37. x = -2, -3
38. x = -1/3, 1
39. Sum = 2, Product = -15
40. No real roots
41. x = -4, -5
42. x = 5, 2
43. x = 3/2
44. Sum = -5/2
45. Product = 2
46. x = 2, 3
47. x = -3, -5
48. No real roots
49. x = 1/2, 3
50. x = 6, -2
51. Sum = -3, Product = -10
52. x = 3, -3
53. x = -3
54. x = -2/3, -2
55. x = 1/2, 1
56. Real roots
57. x = 3, -2
58. x = 4, 5
59. No real roots
60. x = 1/2, 3
61. x = 2, 4
62. x = 1, -1
63. x = 2
64. x = 4, -3

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