SSC CGL - Algebra and Quadratic Equations Online Test (MCQ Quiz)

1. If x + 1/x = 3, then what is the value of x^2 + 1/x^2?

A) 5 B) 7 C) 9 D) 11

2. Solve the quadratic equation: x^2 - 5x + 6 = 0

A) x = 1, x = 6 B) x = 2, x = 3 C) x = -2, x = -3 D) x = -1, x = -6

3. What is the sum of the roots of the quadratic equation ax^2 + bx + c = 0?

A) c/a B) -b/a C) b/a D) -c/a

4. If a quadratic equation has roots 3 and -5, what is the equation?

A) x^2 + 2x - 15 = 0 B) x^2 - 2x - 15 = 0 C) x^2 + 2x + 15 = 0 D) x^2 - 2x + 15 = 0

5. What is the product of the roots of the quadratic equation ax^2 + bx + c = 0?

A) -b/a B) c/a C) b/a D) -c/a

6. If x - 1/x = 5, then what is the value of x^2 + 1/x^2?

A) 23 B) 25 C) 27 D) 29

7. For the quadratic equation 2x^2 - 7x + 3 = 0, find the nature of the roots.

A) Real and distinct B) Real and equal C) Complex D) One real, one complex

8. If x = 2 is a root of the quadratic equation x^2 - kx + 8 = 0, find the value of k.

A) 4 B) 5 C) 6 D) 8

9. What is the discriminant of the quadratic equation ax^2 + bx + c = 0?

A) b^2 - 4ac B) b^2 + 4ac C) 4ac - b^2 D) sqrt(b^2 - 4ac)

10. If x^2 - 9 = 0, what are the values of x?

A) 3 B) -3 C) 3, -3 D) 9

11. If x + y = 7 and xy = 12, find the value of x^2 + y^2.

A) 25 B) 30 C) 35 D) 40

12. Solve for x: 3x^2 - 10x + 7 = 0

A) x = 1, x = 7/3 B) x = -1, x = -7/3 C) x = 1, x = -7/3 D) x = -1, x = 7/3

13. If x^3 = 8, what is the real value of x?

A) 2 B) -2 C) 4 D) 1

14. What is the smallest root of the equation x^2 - 4x + 3 = 0?

A) 1 B) 3 C) -1 D) -3

15. If x = 5, what is the value of x^2 - 2x + 1?

A) 16 B) 20 C) 24 D) 36

16. If x^2 + 1/x^2 = 18, and x is positive, find the value of x + 1/x.

A) 4 B) 5 C) 6 D) 7

17. Find the roots of the quadratic equation x^2 + 4x + 4 = 0.

A) x = 2 B) x = -2 C) x = 2, x = -2 D) x = 4

18. If x^2 - 5x + 6 = 0, what is the value of x(x-5)?

A) -6 B) 6 C) 5 D) -5

19. If x^2 + y^2 = 25 and x + y = 7, find the value of xy.

A) 6 B) 12 C) 18 D) 24

20. What is the value of x if x^2 = 16?

A) 4 B) -4 C) 4, -4 D) 8

21. If x^3 - 1 = 0, what is the real value of x?

A) 1 B) -1 C) 0 D) 3

22. Find the sum of the roots of the equation x^2 - 11x + 30 = 0.

A) 11 B) -11 C) 30 D) -30

23. If x + 1/x = 2, what is the value of x^n + 1/x^n for any positive integer n?

A) 2 B) 0 C) 1 D) n

24. Solve for x: x^2 - 6x + 9 = 0

A) x = 3 B) x = -3 C) x = 3, x = -3 D) x = 9

25. If x^2 - 4 = 0, what is the value of x^2?

A) 2 B) 4 C) 8 D) 16

26. If x - 1/x = 3, what is the value of x^3 - 1/x^3?

A) 18 B) 27 C) 36 D) 54

27. What are the roots of the quadratic equation 3x^2 + 5x - 2 = 0?

A) x = 1/3, x = -2 B) x = -1/3, x = 2 C) x = 2/3, x = -1 D) x = -2/3, x = 1

28. If x^2 + 1/x^2 = 47, find the value of x - 1/x (assuming x > 1).

A) 5 B) 6 C) 7 D) 8

29. What is the value of x^2 - y^2 if x + y = 10 and x - y = 4?

A) 14 B) 40 C) 60 D) 100

30. If x^2 + 2x + 1 = 0, what is the value of x?

A) 1 B) -1 C) 0 D) 2

31. If x^3 = 27, what is the value of x?

A) 3 B) 9 C) 81 D) 27

32. Find the product of the roots of x^2 + 8x + 15 = 0.

A) 8 B) -8 C) 15 D) -15

33. If x + 1/x = 4, what is the value of x^2 + 1/x^2?

A) 14 B) 16 C) 18 D) 20

34. Solve the equation: (x - 2)(x + 3) = 0

A) x = 2, x = -3 B) x = -2, x = 3 C) x = 2, x = 3 D) x = -2, x = -3

35. If x^2 - 10x + 25 = 0, what is the value of x?

A) 5 B) -5 C) 25 D) 10

36. What is the sum of squares of the roots of x^2 - 5x + 6 = 0?

A) 13 B) 25 C) 36 D) 5

37. If x^2 = 49, what is the value of x?

A) 7 B) -7 C) 7, -7 D) 49

38. If x + y = 11 and x^2 + y^2 = 61, find the value of xy.

A) 20 B) 25 C) 30 D) 35

39. If x^3 = 64, what is the real value of x?

A) 4 B) 8 C) 16 D) 64

40. Find the roots of the quadratic equation x^2 - 7x + 10 = 0.

A) x = 2, x = 5 B) x = -2, x = -5 C) x = 2, x = -5 D) x = -2, x = 5

41. If x + 1/x = 5, what is the value of x^3 + 1/x^3?

A) 110 B) 125 C) 130 D) 140

42. What is the smallest integer value of x for which x^2 - 5x + 6 < 0?

A) 0 B) 1 C) 2 D) 3

43. If x^2 = 100, what is the value of x?

A) 10 B) -10 C) 10, -10 D) 20

44. If x^2 - 8x + 16 = 0, what is the value of x?

A) 4 B) -4 C) 8 D) 16

45. If x^2 + 1/x^2 = 22, and x is positive, find the value of x + 1/x.

A) 4 B) 5 C) 6 D) 7

46. Solve for x: 2x^2 + 5x - 3 = 0

A) x = 1/2, x = -3 B) x = -1/2, x = 3 C) x = 3/2, x = -1 D) x = -3/2, x = 1

47. If x^2 - 36 = 0, what are the values of x?

A) 6 B) -6 C) 6, -6 D) 36

48. What is the nature of the roots of the quadratic equation x^2 + x + 1 = 0?

A) Real and distinct B) Real and equal C) Complex conjugates D) One real, one imaginary

49. If x = 3, what is the value of x^3 - 3x^2 + 3x - 1?

A) 7 B) 8 C) 9 D) 10

50. If x^2 + 1/x^2 = 11, what is the value of x + 1/x (assuming x is positive)?

A) 3 B) sqrt(11) C) sqrt(13) D) 4

Algebra and Quadratic Equations - Online Test

Test Results