Tag: Quadratic Expressions

Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers all essential topics of quadratic equations including factorization, roots, discriminant, nature of roots, relations between roots, and application-based problems. Perfect for exam practice, self-assessment, and revision before your Class 10 exams.

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MCQs – Quadratic Equations

1. If the roots of $x^2 – 5x + 6 = 0$x2−5x+6=0 are α and β, then α + β = ?
   A. 5
   B. 6
   C. −5
   D. −6
2. If one root of $x^2 – 7x + k = 0$x2−7x+k=0 is 3, the value of k is:
   A. 10
   B. 12
   C. 15
   D. 21
3. The roots of $2x^2 – 7x + 3 = 0$2×2−7x+3=0 are:
   A. 1, 3/2
   B. 3, 1/2
   C. 3/2, 1
   D. −1, 3
4. For $x^2 + 4x + 5 = 0$x2+4x+5=0, the discriminant is:
   A. 4
   B. −4
   C. −1
   D. 0
5. If the roots of $x^2 – 8x + 15 = 0$x2−8x+15=0 are in the ratio 3:2, then the roots are:
   A. 3, 5
   B. 3, 2
   C. 6, 10
   D. 5, 3
6. Which of the following has equal roots?
   A. $x^2 – 6x + 9 = 0$x2−6x+9=0
   B. $x^2 – 7x + 12 = 0$x2−7x+12=0
   C. $x^2 – 5x + 6 = 0$x2−5x+6=0
   D. $x^2 + 3x + 2 = 0$x2+3x+2=0
7. If α and β are roots of $x^2 – 5x + 6 = 0$x2−5x+6=0, then αβ = ?
   A. 6
   B. 5
   C. −6
   D. 1
8. Sum of roots of $3x^2 – 12x + 9 = 0$3×2−12x+9=0 is:
   A. 3
   B. 4
   C. 12
   D. −4
9. One root of $x^2 – 9x + 14 = 0$x2−9x+14=0 is 7. The other root is:
   A. 2
   B. 3
   C. 4
   D. 5
10. If the roots of $x^2 + 2x – 15 = 0$x2+2x−15=0 are α and β, then α − β = ?
    A. 8
    B. 7
    C. 6
    D. 5
11. Quadratic equation whose roots are 2 and −3 is:
    A. $x^2 + x − 6 = 0$x2+x−6=0
    B. $x^2 − x − 6 = 0$x2−x−6=0
    C. $x^2 + x + 6 = 0$x2+x+6=0
    D. $x^2 − 5x + 6 = 0$x2−5x+6=0
12. If the roots of $x^2 + kx + 12 = 0$x2+kx+12=0 are equal, k = ?
    A. 4
    B. −4
    C. 6
    D. −6
13. If α and β are roots of $x^2 − 4x + 3 = 0$x2−4x+3=0, then 1/α + 1/β = ?
    A. 4/3
    B. 3/4
    C. 1
    D. −1
14. If one root of $x^2 + px + 2 = 0$x2+px+2=0 is 2, find p.
    A. −3
    B. 3
    C. −4
    D. 4
15. Roots of $x^2 + 5x + 6 = 0$x2+5x+6=0 are:
    A. −2, −3
    B. 2, 3
    C. −1, −6
    D. 1, 6
16. If roots of $2x^2 − 7x + 3 = 0$2×2−7x+3=0 are α and β, then α/β + β/α = ?
    A. 7/3
    B. 17/6
    C. 13/6
    D. 3/2
17. α² + β² if α and β are roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 13
    B. 25
    C. 11
    D. 10
18. Roots of $x^2 − 3x − 10 = 0$x2−3x−10=0 are in AP. The roots are:
    A. −2, 5
    B. 2, −5
    C. 5, −2
    D. −5, 2
19. Equation whose roots are reciprocals of roots of $x^2 − 4x + 3 = 0$x2−4x+3=0 is:
    A. $3x^2 − 4x + 1 = 0$3×2−4x+1=0
    B. $x^2 − 3x + 4 = 0$x2−3x+4=0
    C. $x^2 − 4x + 3 = 0$x2−4x+3=0
    D. $4x^2 − 3x + 1 = 0$4×2−3x+1=0
20. Roots of $x^2 − x − 6 = 0$x2−x−6=0 are:
    A. 3, −2
    B. −3, 2
    C. 2, −3
    D. −2, 3
21. If sum of roots of $x^2 − kx + 12 = 0$x2−kx+12=0 is 7, then k = ?
    A. 7
    B. −7
    C. 12
    D. −12
22. One root of $x^2 − 8x + 12 = 0$x2−8x+12=0 is 6. The other root is:
    A. 2
    B. 3
    C. 4
    D. 5
23. $x^2 − 2kx + k = 0$x2−2kx+k=0 has equal roots for k = ?
    A. 1
    B. 2
    C. 4
    D. 0
24. Sum of squares of roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 25
    B. 13
    C. 11
    D. 6
25. If roots of $x^2 − 6x + 8 = 0$x2−6x+8=0 are α and β, 1/α + 1/β = ?
    A. 3/4
    B. 4/3
    C. 1
    D. 2
26. Roots of $x^2 − x − 12 = 0$x2−x−12=0 are:
    A. 4, −3
    B. −4, 3
    C. 3, −4
    D. −3, 4
27. One root of $2x^2 − 5x + 2 = 0$2×2−5x+2=0 is 2. The other root is:
    A. 1/2
    B. 1
    C. 2
    D. −1
28. Product of roots of $x^2 − 7x + 12 = 0$x2−7x+12=0 is:
    A. 12
    B. 7
    C. −12
    D. 5
29. Roots of $x^2 − 2x − 15 = 0$x2−2x−15=0 are:
    A. 5, −3
    B. −5, 3
    C. 3, −5
    D. −3, 5
30. One root of $x^2 − kx + 16 = 0$x2−kx+16=0 is 4. The other root is:
    A. 4
    B. 12
    C. k − 4
    D. 16
31. Quadratic equation with roots 1/2 and 1/3 is:
    A. $6x^2 − 5x + 1 = 0$6×2−5x+1=0
    B. $2x^2 − 5x + 6 = 0$2×2−5x+6=0
    C. $x^2 − 5x + 6 = 0$x2−5x+6=0
    D. $3x^2 − 5x + 2 = 0$3×2−5x+2=0
32. If α and β are roots of $x^2 − 3x + 2 = 0$x2−3x+2=0, then 1/α² + 1/β² = ?
    A. 5/4
    B. 1/4
    C. 4/5
    D. 2/3
33. One root of $x^2 − 5x + k = 0$x2−5x+k=0 is twice the other, k = ?
    A. 0
    B. 2
    C. 4
    D. 6
34. If roots of $x^2 − x − 6 = 0$x2−x−6=0 are α and β, then α³ + β³ = ?
    A. 35
    B. 27
    C. 28
    D. 26
35. Quadratic equation whose roots differ by 1 and sum to 7 is:
    A. $x^2 − 7x + 12 = 0$x2−7x+12=0
    B. $x^2 − 6x + 12 = 0$x2−6x+12=0
    C. $x^2 − 7x + 10 = 0$x2−7x+10=0
    D. $x^2 − 6x + 10 = 0$x2−6x+10=0
36. α³ + β³ if α and β are roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 50
    B. 35
    C. 40
    D. 30
37. If roots of $x^2 + px + q = 0$x2+px+q=0 are equal, then p² − 4q = ?
    A. 0
    B. 1
    C. 2
    D. −1
38. One root of $x^2 − 4x + 4 = 0$x2−4x+4=0 is:
    A. 2
    B. 4
    C. 1
    D. 0
39. α² + β² if α and β are roots of $x^2 + 3x + 2 = 0$x2+3x+2=0 is:
    A. 1
    B. 5
    C. 13
    D. 9
40. One root of $x^2 − 7x + 12 = 0$x2−7x+12=0 is 3. The other root is:
    A. 4
    B. 5
    C. 6
    D. 2
41. Roots of $x^2 − 6x + 5 = 0$x2−6x+5=0 are:
    A. 1, 5
    B. −1, 5
    C. 1, −5
    D. −1, −5
42. Sum of squares of roots of $x^2 − 10x + 21 = 0$x2−10x+21=0 is:
    A. 50
    B. 58
    C. 49
    D. 60
43. Roots of $x^2 − 2x − 3 = 0$x2−2x−3=0 are:
    A. 3, −1
    B. −3, 1
    C. 1, −3
    D. −1, 3
44. Roots of $x^2 − 5x + 4 = 0$x2−5x+4=0 are:
    A. 4, 1
    B. 1, 4
    C. −1, 4
    D. 2, 2
45. If one root of $x^2 − 8x + 15 = 0$x2−8x+15=0 is 3, the other root is:
    A. 5
    B. 6
    C. 4
    D. 2

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Answers – List Form

1. A
2. C
3. C
4. B
5. A
6. A
7. A
8. B
9. A
10. B
11. A
12. B
13. A
14. A
15. A
16. B
17. C
18. A
19. A
20. A
21. A
22. A
23. B
24. B
25. B
26. A
27. A
28. A
29. B
30. C
31. A
32. A
33. C
34. A
35. A
36. A
37. A
38. A
39. B
40. A
41. A
42. C
43. A
44. A
45. A