Class 10 Mathematics Chapter 2: Theory of Quadratic Equations – MCQs

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 the theory and properties of quadratic equations, including discriminant, nature of roots, relation between roots and coefficients, factorization, sum and product of roots, and application-based problems. It is ideal for exam revision and self-assessment.

MCQs – Theory of Quadratic Equations (Class 10)

1. If α and β are roots of $x^2 − 5x + 6 = 0$x2−5x+6=0, then α + β = ?
   A. 5
   B. 6
   C. −5
   D. −6
2. If the roots of $x^2 − kx + 12 = 0$x2−kx+12=0 are equal, k = ?
   A. 6
   B. 8
   C. 4
   D. −4
3. Discriminant of $x^2 − 4x + 5 = 0$x2−4x+5=0 is:
   A. −4
   B. 4
   C. 0
   D. −1
4. The roots of $x^2 − 7x + 12 = 0$x2−7x+12=0 are:
   A. 3, 4
   B. 4, 3
   C. −3, −4
   D. 2, 6
5. If one root of $x^2 − 6x + 5 = 0$x2−6x+5=0 is 1, the other root is:
   A. 5
   B. −5
   C. 6
   D. 4
6. Product of roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
   A. 6
   B. 5
   C. −6
   D. −5
7. Sum of roots of $3x^2 − 12x + 9 = 0$3×2−12x+9=0 is:
   A. 4
   B. 3
   C. −4
   D. 12
8. Roots of $x^2 + 4x + 4 = 0$x2+4x+4=0 are:
   A. −2, −2
   B. 2, 2
   C. 2, −2
   D. −4, 1
9. If 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. 5, 3
   C. 6, 10
   D. 2, 3
10. If α and β are roots of $x^2 − 3x − 10 = 0$x2−3x−10=0, then αβ = ?
    A. −10
    B. 10
    C. 3
    D. −3
11. If one root of $x^2 − 7x + 12 = 0$x2−7x+12=0 is 4, the other root is:
    A. 3
    B. 2
    C. 5
    D. 6
12. Sum of squares of roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 11
    B. 10
    C. 13
    D. 12
13. If α and β are roots of $x^2 + 3x − 4 = 0$x2+3x−4=0, then 1/α + 1/β = ?
    A. −3/4
    B. 3/4
    C. 1
    D. −1
14. Quadratic equation whose roots are 2 and 3 is:
    A. $x^2 − 5x + 6 = 0$x2−5x+6=0
    B. $x^2 + 5x − 6 = 0$x2+5x−6=0
    C. $x^2 − x − 6 = 0$x2−x−6=0
    D. $x^2 − 6x + 5 = 0$x2−6x+5=0
15. Roots of $x^2 − 4x + 3 = 0$x2−4x+3=0 are:
    A. 1, 3
    B. 3, 1
    C. −1, −3
    D. 2, 3
16. Nature of roots of $x^2 + x + 1 = 0$x2+x+1=0 is:
    A. Complex
    B. Real and equal
    C. Real and distinct
    D. Zero
17. If α + β = 7 and αβ = 12, the quadratic equation is:
    A. $x^2 − 7x + 12 = 0$x2−7x+12=0
    B. $x^2 + 7x + 12 = 0$x2+7x+12=0
    C. $x^2 − 12x + 7 = 0$x2−12x+7=0
    D. $x^2 + 12x + 7 = 0$x2+12x+7=0
18. If roots of $x^2 − 2x − 8 = 0$x2−2x−8=0 are α and β, then α − β = ?
    A. 4
    B. 6
    C. 2√3
    D. √12
19. One root of $x^2 − 9x + 20 = 0$x2−9x+20=0 is 4. The other root is:
    A. 5
    B. 4
    C. 6
    D. 3
20. Quadratic equation with roots −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. $x^2 − x + 6 = 0$x2−x+6=0
21. If α and β are roots of $x^2 − 5x + 6 = 0$x2−5x+6=0, then α² + β² = ?
    A. 13
    B. 11
    C. 10
    D. 12
22. One root of $x^2 − 6x + 8 = 0$x2−6x+8=0 is 2. The other root is:
    A. 4
    B. 2
    C. 6
    D. 3
23. Roots of $x^2 − x − 6 = 0$x2−x−6=0 are:
    A. 3, −2
    B. −3, 2
    C. 2, −3
    D. −2, 3
24. If roots of $x^2 + 2x − 15 = 0$x2+2x−15=0 are α and β, then α³ + β³ = ?
    A. 50
    B. 35
    C. 40
    D. 45
25. If roots of $x^2 − 7x + 12 = 0$x2−7x+12=0 are equal, then discriminant is:
    A. 0
    B. 1
    C. −1
    D. 2
26. If one root of $x^2 − kx + 16 = 0$x2−kx+16=0 is 4, the other root is:
    A. 4
    B. k − 4
    C. 2
    D. 3
27. Sum of reciprocals of roots of $x^2 − 3x − 4 = 0$x2−3x−4=0 is:
    A. 3/−4
    B. −3/4
    C. −4/3
    D. 4/3
28. If α = 2β and α + β = 6, the roots of the quadratic are:
    A. 4, 2
    B. 2, 4
    C. 3, 1
    D. 1, 3
29. Roots of $x^2 + 5x + 6 = 0$x2+5x+6=0 are:
    A. −2, −3
    B. 2, 3
    C. −1, −6
    D. 1, 6
30. One root of $x^2 − 5x + 6 = 0$x2−5x+6=0 is 3. The other root is:
    A. 2
    B. 3
    C. 1
    D. 4
31. αβ if α and β are roots of $x^2 − 8x + 12 = 0$x2−8x+12=0 is:
    A. 12
    B. 8
    C. 10
    D. 6
32. Nature of roots of $x^2 − 4x + 4 = 0$x2−4x+4=0 is:
    A. Equal and real
    B. Distinct and real
    C. Complex
    D. Zero
33. α + β if α and β are roots of $x^2 − 6x + 5 = 0$x2−6x+5=0 is:
    A. 6
    B. 5
    C. 1
    D. 11
34. Roots of $x^2 − 10x + 21 = 0$x2−10x+21=0 are:
    A. 3, 7
    B. 7, 3
    C. −3, −7
    D. 5, 6
35. Sum of squares of roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 13
    B. 11
    C. 10
    D. 12
36. One root of $x^2 − 2x − 8 = 0$x2−2x−8=0 is 4. The other root is:
    A. −2
    B. 2
    C. −4
    D. 2
37. If α + β = 7, αβ = 12, then quadratic equation is:
    A. $x^2 − 7x + 12 = 0$x2−7x+12=0
    B. $x^2 + 7x + 12 = 0$x2+7x+12=0
    C. $x^2 − 12x + 7 = 0$x2−12x+7=0
    D. $x^2 + 12x + 7 = 0$x2+12x+7=0
38. α² − β² if α = 3, β = 1 is:
    A. 8
    B. 4
    C. 2
    D. 1
39. Quadratic equation whose roots are reciprocals of 2 and 3 is:
    A. $6x^2 − 5x + 1 = 0$6×2−5x+1=0
    B. $x^2 − 5x + 6 = 0$x2−5x+6=0
    C. $2x^2 − 5x + 6 = 0$2×2−5x+6=0
    D. $3x^2 − 5x + 2 = 0$3×2−5x+2=0
40. Roots of $x^2 − 3x + 2 = 0$x2−3x+2=0 are:
    A. 1, 2
    B. 2, 1
    C. −1, −2
    D. 3, 2
41. If one root of $x^2 − 6x + 9 = 0$x2−6x+9=0 is 3, the other root is:
    A. 3
    B. −3
    C. 2
    D. 1
42. α/β + β/α if α and β are roots of $x^2 − 5x + 6 = 0$x2−5x+6=0 is:
    A. 17/6
    B. 13/6
    C. 3/2
    D. 7/3
43. Roots of $x^2 − 8x + 16 = 0$x2−8x+16=0 are:
    A. 4, 4
    B. 8, 2
    C. 2, 8
    D. −4, 4
44. One root of $x^2 − 7x + 12 = 0$x2−7x+12=0 is 4. The other root is:
    A. 3
    B. 2
    C. 5
    D. 6
45. If α + β = 5, αβ = 6, quadratic equation is:
    A. $x^2 − 5x + 6 = 0$x2−5x+6=0
    B. $x^2 + 5x + 6 = 0$x2+5x+6=0
    C. $x^2 − 6x + 5 = 0$x2−6x+5=0
    D. $x^2 + 6x + 5 = 0$x2+6x+5=0

Answers – List Form

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