Mathematics Quadratic Equations Online Mcqs Test

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Question 1

1. If a > 0, then function f(x) = ax² + bx + c has minimum value at

Answer

x = - a/2b

Answer

None of these

Answer

x = - b/2a

Question 2

2. The quadratic equation whose roots are α β is

Answer

x² + (α + β)x + αβ = 0

Answer

x² - (α + β)x + αβ = 0

Answer

x² - (α + β)x - αβ = 0

Answer

x² + (α + β)x - αβ = 0

Question 3

3. If P(x) is divided by x – r such that Q(x) is the quotient and R is the remainder, then the division algorithm is

Answer

P(x) = (x – r)Q (x) + R

Answer

P(x) = (x – r)R + Q(x)

Answer

Q(x) = (x – r)P (x) + R

Answer

Q(x) = (x – r)R + P(x)

Question 4

4. If the roots of ax² + bx + c = 0 are equal in magnitude but opposite in sign, then

Answer

None of these

Question 5

5. If x³ + 3x² - 6x + 2 is divided by x + 2, then the remainder is

Question 6

6. Both the roots of the equation (x – b)(x – c) + (x – c)(x – a) + (x – a)(x – b) = 0 are always

Answer

None of these

Question 7

7. For a quadratic equation ax² + bx + c sum of the root is

Answer

None of these

Question 8

8. If x⁴ – 3x + 5 is divided by 2x – 1, then the remainder is

Question 9

9. If 9x³ - 5x² is divided by 3x + 1, then the remainder is

Answer

None of these

Question 10

10. ax⁴ + bx³ + cx² + bx + a = 0 is called _________ equation

Answer

Reciprocal

Answer

Exponential

Question 11

11. 3 x 2 + 2x + 1 is a

Answer

Polynomial of degree 3

Answer

Polynomial of degree 0

Answer

Polynomial of degree n

Answer

Polynomial of degree 2

Question 12

12. If x – 2 is a factor of ax² – 12x + 4, then

Question 13

13. The value of p for which both the roots of the equation 4x² – 20 px + (25p² + 15p – 66) = 0 are less than 2, lies in

Answer

(-∞, -1)

Answer

(-1, -4/5)

Question 14

14. A root of equation x⁴ - 5x² + 4 = 0 is

Answer

None of these

Question 15

15. 7y2 + 5 √y + 3 is a polynomial over

Answer

Natural numbers

Answer

None of these

Answer

Rational number

Question 16

16. The nature of the roots of equation 9x² -5x + 3 = 0

Answer

Irrational

Answer

Real & equal

Answer

Real & unequal

Question 17

17. The roots of the equation 2²x – 10.2x + 16 = 0 are

Question 18

18. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

Question 19

19. The solution of a quadratic equation x² + 5x – 6 = 0

Answer

x = -1, x = 6

Answer

x = 1, x = -6

Question 20

20. The quadratic equation 8 sec²θ – 6 sec θ + 1 = 0 has

Answer

Exactly four roots

Answer

Exactly two roots

Answer

Infinitely many roots

Question 21

21. w¹⁰⁹ = ?

Answer

[-1+i√3/2]

Answer

[-1-√3/2]

Question 22

22. If ω is the imaginary cube root of unity, then the cube rots of 125 are

Answer

3,3 ω, 3 ω²

Answer

-5, -5 ω, -5 ω²

Answer

5, 5 ω, 5 ω²

Answer

-3, -3 ω, -3 ω²

Question 23

23. If α, β are non-real roots of ax² + bx + c = 0 (a, b, c ϵ Q), then

Question 24

24. If one root of the equation ax² + bx + c = 0, a ≠ 0, be reciprocal of the other, then

Question 25

25. 3x⁴ + √5 x² + 3x + 1 is a polynomial of degree

Question 26

26. For a quadratic equation ax² + bx + c = 0, the sum of roots is

Question 27

27. If one root of the equation ix² – 2 (i + 1) x + (2 – i) = 0 is 2 – i, then the other root is

Question 28

28. The roots of the quadratic equation ax2 + bx + c = 0 are real and distinct if.

Answer

b² – 4ac = 0

Answer

b² – 4ac < 0

Answer

b² – 4ac > 0

Answer

None of these

Question 29

29. The product of the roots of equation px² – tx + n = 0 is

Answer

None of these

Question 30

30. If the roots of ax² + b = 0 are real and distinct then

Answer

a > 0, b > 0

Question 31

31. Quadratic equation is an equation of degree

Question 32

32. If the roots of 3x² + kx + 12 = 0 are equal, then k =

Question 33

33. Cube roots of -64 are

Answer

-4, w, w²

Answer

4, 4w, 4w²

Answer

-4, -4w, -4w²

Question 34

34. If a polynomial f(x) is divided by a linear divisor ax + 1, the remainder is

Question 35

35. The condition for polynomial equation ax² + bx + c = 0 to be quadratic is

Answer

a ≠ 0, b ≠ 0

Question 36

36. If S = the sum of the roots of the equation and P = product of the roots of the equation then their equation can be written as:

Answer

x² + Sx – P = 0

Answer

x² – Sx – P = 0

Answer

x² – Sx + P = 0

Answer

x² + Sx + P = 0

Question 37

37. The roots of the quadratic equation 2x² – 5x + 3 – 0 are

Answer

Irrational

Question 38

38. What should be added to 9x⁴ + 2x² + 25 to make it a perfect square?

Question 39

39. x² + 4x + 4 is

Answer

Polynomial

Answer

None of these

Question 40

40. If ω is the imaginary cube root of unity, then ω³ =

Question 41

41. If α, β are the roots of ax² + bx + c = 0, then roots of cx² + bx + a = 0 are

Answer

1/α, 1/β

Question 42

42. Which statement is true about the discriminant of the quadratic equation cx² + dx + e = 0 when c ≠ 0?

Answer

None of these

Answer

d² – 4ce

Question 43

43. If 2, 3 are roots of the equation 2x³ + mx² – 3x + n 0, then the value of m and n are.

Answer

–5, – 30

Answer

None of these

Question 44

44. What is the type of equation 14(x⁴+1) – 7(x³ + x) + 8x² = 0?

Answer

None of these

Answer

Reciprocal

Answer

Irrational

Question 45

45. 3x² + 2x + 1 is a

Answer

Polynomial of degree 3

Answer

Polynomial of degree 0

Answer

Polynomial of degree n

Answer

Polynomial of degree 2

Question 46

46. If x³ + ax + – a²x – a³ is divided by x + a, then the remainder is

Question 47

47. The solution set of x² + 4x – 437 = 0 is

Question 48

48. 1+w+w² = ?

Answer

None of these

Question 49

49. The polynomial ax³ + bx² + 8 has degree

Answer

None of these

Question 50

50. A polynomial having one term is called

Answer

None of these

Question 51

51. The value of a for which the sum of the squares of the roots of the equation x² – (a – 2) x – 1 = 0 assume the least value is

Question 52

52. If a > 0, b > 0, c > 0, then the roots of the equation ax² + bx + c = 0 are

Answer

Nothing can be said

Answer

Real and negative

Answer

Real and positive

Answer

Non-real with negative real parts

Question 53

53. If the sum and product of the roots an equation are b/a, c²/b, then the quadratic equation is

Answer

ab² – bx + c = 0

Answer

x² – bx + ac

Answer

abx² – b²x + ac² = 0

Answer

abx² – x + ac² = 0

Question 54

54. The quadratic formula is

Question 55

55. If for the quadratic equation ax² + bx + c = 0, the difference of the roots is the same as their product, then the ration of the roots is.

Answer

b – c/b + c

Answer

c – a/c + a

Answer

None of these

Answer

a – b/a + b

Question 56

56. If x² - 7x + a has a remainder 1 when divided by x + 1, then

Question 57

57. The quadratic equation with roots 2 - √3 and 2 + √3 is

Answer

x² - 4x + 1 = 0

Answer

x² - 6x – 6 = 0

Answer

x² - 6x + 6 = 0

Answer

x² + 4x + 1 = 0

Question 58

58. The roots of (x – a)(x – b) = ab x² are always

Answer

Depends upon b

Answer

Depends upon a

Answer

Depends upon a and b

Question 59

59. The product of the roots of the equation 9x² – 5x – 27 = 0

Question 60

60. If the roots of p² + qx + 1 = 0 are equal, then

Answer

q² + 4p = 0

Answer

q² - 4p = 0

Answer

p² - 4p = 0

Answer

p² + 4q = 0

Question 61

61. If one root of the equation x² – 3x + a = 0 is 2, then

Question 62

62. The four fourth roots of unity are

Answer

-3, 3, -3i, 3i

Answer

-2, -2, -2i, 2i

Answer

-1,1, -i, i

Answer

-4, 4, -4i, 4i

Question 63

63. The first degree function are called function

Answer

None of these

Question 64

64. If α and β are the roots of x² – 2x + 3 = 0, then the equation with roots α + 2, β + 2 is

Answer

x² – 6x + 11 = 0

Answer

3x² – 2x + 1 = 0

Answer

x² – 11x + 6 = 0

Answer

x² – 6x – 11

Answer 106

>0 and is a perfect square

Answer 107

b = 0, c = 0

Answer 108

a = b = c = 0

Answer 109

Polynomial of degree 3

Answer 110

Polynomial of degree 2

Answer 111

Polynomial of degree n

Answer 112

Polynomial of degree 0

Answer 113

b = 0, c ≠ 0

Answer 114

c = 0, b ≠ 0

Answer 115

b = 0, c = 0

Answer 116

x² + Sx + P = 0

Answer 117

x² – Sx + P = 0

Answer 118

x² – Sx – P = 0

Answer 119

x² + Sx – P = 0

Answer 120

Irrational

Answer 121

Reciprocal

Answer 122

None of these

Answer 123

None of these

Total Questions:	79
Time Allowed:	40 Minutes
Total Marks:	79
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Important Math Quadratic Equations Question and Answer

Math Quadratic Equations Practice Test Online With Explanation

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