SSC CGL - Quadratic Equations Online Test (MCQ Quiz)

1. What is the standard form of a quadratic equation?

A) ax + b = 0 B) ax^2 + bx + c = 0 C) ax^3 + bx^2 + cx + d = 0 D) a/x + b = 0

2. In a quadratic equation ax^2 + bx + c = 0, what condition must 'a' satisfy?

A) a = 0 B) a != 0 C) a > 0 D) a < 0

3. Which of the following is a method to solve quadratic equations?

A) Graphical method B) Completing the square C) Factoring D) All of the above

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

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

5. If the discriminant (D = b^2 - 4ac) of a quadratic equation is positive (D > 0), what type of roots does it have?

A) Two equal real roots B) Two distinct real roots C) No real roots (two complex roots) D) One real root

6. If the discriminant (D = b^2 - 4ac) of a quadratic equation is zero (D = 0), what type of roots does it have?

A) Two distinct real roots B) Two equal real roots C) No real roots D) One complex root

7. If the discriminant (D = b^2 - 4ac) of a quadratic equation is negative (D < 0), what type of roots does it have?

A) Two distinct real roots B) Two equal real roots C) No real roots (two complex conjugate roots) D) One real root

8. What are the roots of the quadratic equation x^2 - 5x + 6 = 0?

A) 2 and 3 B) 1 and 6 C) -2 and -3 D) 1 and 5

9. What are the roots of the quadratic equation x^2 + 4x + 4 = 0?

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

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

A) 1 + 2i and 1 - 2i B) 2 + i and 2 - i C) 1 + i and 1 - i D) 2 and -1

11. For the quadratic equation ax^2 + bx + c = 0, what is the sum of the roots?

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

12. For the quadratic equation ax^2 + bx + c = 0, what is the product of the roots?

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

13. If one root of the quadratic equation x^2 - 6x + k = 0 is 2, what is the value of k?

A) 8 B) -8 C) 6 D) -6

14. If the roots of the quadratic equation x^2 - px + 12 = 0 are 3 and 4, what is the value of p?

A) 7 B) -7 C) 12 D) -12

15. Which quadratic equation has roots 5 and -2?

A) x^2 - 3x - 10 = 0 B) x^2 + 3x - 10 = 0 C) x^2 - 3x + 10 = 0 D) x^2 + 3x + 10 = 0

16. Which quadratic equation has roots -1/2 and 1/3?

A) 6x^2 + x - 1 = 0 B) 6x^2 - x - 1 = 0 C) 6x^2 + 5x - 1 = 0 D) 6x^2 - 5x - 1 = 0

17. The equation (x+1)^2 = 9 is a quadratic equation. What are its roots?

A) 2 and -4 B) -2 and 4 C) 3 and -3 D) 1 and -1

18. If x = 2 is a root of 2x^2 - kx + 6 = 0, what is the value of k?

A) 7 B) -7 C) 8 D) -8

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

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

20. What is the nature of the roots of the equation 4x^2 - 12x + 9 = 0?

A) Real and distinct B) Real and equal C) Complex conjugate D) No real roots

21. What is the nature of the roots of the equation 3x^2 - 5x + 2 = 0?

A) Real and distinct B) Real and equal C) Complex conjugate D) No real roots

22. If the roots of ax^2 + bx + c = 0 are a and b, then which of the following is true?

A) a + b = -b/a and ab = c/a B) a + b = b/a and ab = -c/a C) a + b = -c/a and ab = b/a D) a + b = c/a and ab = -b/a

23. What is the value of k for which the equation kx^2 - 5x + k = 0 has equal roots?

A) ±√(5/2) B) ±5/2 C) ±2/5 D) ±√(2/5)

24. If one root of the quadratic equation x^2 - (k+1)x + 6 = 0 is 2, find the other root.

A) 3 B) 4 C) 5 D) 6

25. The sum of the roots of the equation x^2 + 5x + 3 = 0 is:

A) 5 B) -5 C) 3 D) -3

26. The product of the roots of the equation 2x^2 - 7x + 6 = 0 is:

A) 7/2 B) -7/2 C) 3 D) -3

27. Which method involves rewriting the quadratic expression as a perfect square?

A) Factoring B) Quadratic formula C) Completing the square D) Graphical method

28. The equation 3x^2 + 2x - 1 = 0 has roots:

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

29. If the roots of x^2 - ax + b = 0 are m and n, then m+n equals:

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

30. If the roots of x^2 - ax + b = 0 are m and n, then mn equals:

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

31. For the equation x^2 + 4 = 0, what are the roots?

A) 2 and -2 B) 2i and -2i C) 2i and 2i D) 4i and -4i

32. What is the value of k if the quadratic equation x^2 - kx + 4 = 0 has equal roots?

A) ±4 B) ±2 C) ±8 D) ±16

33. If one root of the equation ax^2 + bx + c = 0 is 0, then which coefficient must be zero?

A) a B) b C) c D) a and b

34. The sum of the roots of the equation (x-2)(x+3) = 0 is:

A) 1 B) -1 C) 5 D) -5

35. The product of the roots of the equation (x-2)(x+3) = 0 is:

A) 1 B) -1 C) 5 D) -6

36. What is the quadratic equation whose roots are reciprocals of the roots of x^2 - 5x + 6 = 0?

A) 6x^2 - 5x + 1 = 0 B) 6x^2 + 5x + 1 = 0 C) 5x^2 - 6x + 1 = 0 D) x^2 - 6x + 5 = 0

37. If one root of the equation ax^2 + bx + c = 0 is the square of the other, what is the relation between a, b, and c?

A) b^3 = a(c - ab) B) b^3 = c(a - bc) C) b^3 = a^2c + ac^2 D) b^3 + ac + a^2c^2 = 0

38. The equation x + 1/x = 5 can be written as a quadratic equation. What is it?

A) x^2 - 5x + 1 = 0 B) x^2 + 5x + 1 = 0 C) x^2 - 5x - 1 = 0 D) x^2 + 5x - 1 = 0

39. If the roots of the equation x^2 + bx + c = 0 are equal, then:

A) b^2 = 4c B) b^2 = -4c C) c^2 = 4b D) c^2 = -4b

40. Consider the quadratic equation x^2 - 7x + 10 = 0. What is the difference between its roots?

A) 1 B) 2 C) 3 D) 5

41. If the sum of the roots of a quadratic equation is S and the product is P, the equation can be written as:

A) x^2 + Sx + P = 0 B) x^2 - Sx + P = 0 C) x^2 + Px + S = 0 D) x^2 - Px + S = 0

42. What is the value of k for which the roots of the equation x^2 - (k+2)x + 3k = 0 are equal?

A) 3 B) 6 C) 9 D) 12

43. If one root of the equation x^2 - 3x + k = 0 is 1, what is the value of k?

A) 2 B) -2 C) 3 D) -3

44. The equation 3x^2 - 6x + 2 = 0 has roots α and β. What is the value of α + β?

A) 2 B) -2 C) 6 D) -6

45. The equation 3x^2 - 6x + 2 = 0 has roots α and β. What is the value of αβ?

A) 2/3 B) -2/3 C) 6/3 D) -6/3

46. If the roots of the equation x^2 - 5x + k = 0 are 2 and 3, what is the value of k?

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

47. What is the value of k if the equation x^2 - 4x + k = 0 has roots that are equal?

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

48. If one root of the equation x^2 - (a+1)x + 6 = 0 is 2, find the other root.

A) 3 B) 4 C) 5 D) 6

49. What is the discriminant of the quadratic equation 2x^2 + 5x - 3 = 0?

A) 25 B) 49 C) -25 D) -49

50. Which of the following quadratic equations has roots 1/2 and -1/3?

A) 6x^2 + x - 1 = 0 B) 6x^2 - x - 1 = 0 C) 6x^2 + 5x - 1 = 0 D) 6x^2 - 5x - 1 = 0

Quadratic Equations - Online Test

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