Mathematics Quadratic Equations Online Mcqs Test

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You can prepare for Mathematics Quadratic Equations Online Mcqs Test by attempting the free online quizzes at Gotest.com.pk. We provide instant results, performance reports, and detailed explanations for every question.

Question 1

1. Only one of the root of ax² + bx + c = 0, a ≠ 0, is zero if

Answer

b = 0, c = 0

Answer

b = 0, c ≠ 0

Answer

c = 0, b ≠ 0

Question 2

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

Answer

None of these

Question 3

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

Question 4

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

Answer

None of these

Question 5

5. Which one is true?

Question 6

6. The polynomial ax³ + bx² + 8 has degree

Answer

None of these

Question 7

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

Answer

None of these

Question 8

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

Answer

x = - a/2b

Answer

x = - b/2a

Answer

None of these

Question 9

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

Answer

a > 0, b > 0

Question 10

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

Question 11

11. 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 12

12. 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 13

13. If roots of a quadratic equation are equal then discriminant

Answer

>0 and is a perfect square

Question 14

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

Question 15

15. Cube roots of -64 are

Answer

-4, -4w, -4w²

Answer

-4, w, w²

Answer

4, 4w, 4w²

Question 16

16. 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

Q(x) = (x – r)P (x) + R

Answer

Q(x) = (x – r)R + P(x)

Answer

P(x) = (x – r)R + Q(x)

Question 17

17. The first degree function are called function

Answer

None of these

Question 18

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

Question 19

19. If the roots of x² – 5x + a = 0 are equal, then a =

Answer

None of these

Question 20

20. For S = Sum of roots and P = Product of roots, the quadratic equation is

Answer

x² – Sx – P = 0

Answer

x² + Sx + P = 0

Answer

x² + Sx – P = 0

Answer

x² – Sx + P = 0

Question 21

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

Answer

None of these

Question 22

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

Question 23

23. The quadratic formula is

$Math 4.01$

Question 24

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

Question 25

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

Question 26

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

Answer

5, 5 ω, 5 ω²

Answer

-3, -3 ω, -3 ω²

Answer

3,3 ω, 3 ω²

Answer

-5, -5 ω, -5 ω²

Question 27

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

Question 28

28. Quadratic equation is an equation of degree

Question 29

29. 1+w+w² = ?

Answer

None of these

Question 30

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

Question 31

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

Question 32

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

Question 33

33. 3x² + 2x + 1 is a

Answer

Polynomial of degree 2

Answer

Polynomial of degree n

Answer

Polynomial of degree 0

Answer

Polynomial of degree 3

Question 34

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

Question 35

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

Question 36

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

Answer

Exponential

Answer

Reciprocal

Question 37

37. The four fourth roots of unity are

Answer

-3, 3, -3i, 3i

Answer

-1,1, -i, i

Answer

-4, 4, -4i, 4i

Answer

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

Question 38

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

Question 39

39. 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 40

40. 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

a – b/a + b

Answer

None of these

Answer

c – a/c + a

Answer

b – c/b + c

Question 41

41. Which is the root of the equation x⁴ - 9x³ + 6x² + 2 = 0?

Question 42

42. A polynomial having one term is called

Answer

None of these

Question 43

43. 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, -4/5)

Answer

(-∞, -1)

Question 44

44. If ax² + bx + c = 0 is satisfied by every value of x, then

Answer

a = b = c = 0

Answer

b = 0, c = 0

Question 45

45. Sum of the roots of equation ax² + bx + c = 0 is

Question 46

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

Answer

Depends upon a

Answer

Depends upon b

Answer

Depends upon a and b

Question 47

47. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

Question 48

48. Name the type of equation √x+a + √x+b = e√ex+d

Answer

Reciprocal

Answer

Irrational

Answer

None of these

Question 49

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

Answer

a ≠ 0, b ≠ 0

Question 50

50. 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 51

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

Answer

Irrational

Answer

None of these

Answer

Reciprocal

Question 52

52. w¹⁰⁹ = ?

Answer

[-1+i√3/2]

Answer

[-1-√3/2]

Question 53

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

Answer

b² – 4ac > 0

Answer

None of these

Answer

b² – 4ac = 0

Answer

b² – 4ac < 0

Question 54

54. x³ – 3x² + 2x – 6 has a factor

Question 55

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

Answer

Irrational

Answer

Real & equal

Answer

Real & unequal

Question 56

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

Question 57

57. Two square roots of the unity are

Question 58

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

Answer

None of these

Answer

–5, – 30

Question 59

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

Answer

Irrational

Question 60

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

Question 61

61. 3 x 2 + 2x + 1 is a

Answer

Polynomial of degree 0

Answer

Polynomial of degree 2

Answer

Polynomial of degree n

Answer

Polynomial of degree 3

Question 62

62. If n is a nonnegative integer, Then a₀xⁿ + …. + a₁x +a₀ is a

Answer

Polynomial of degree 3

Answer

Polynomial of degree 2

Answer

Polynomial of degree n

Answer

Polynomial of degree 0

Question 63

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

Answer

x = 1, x = -6

Answer

x = -1, x = 6

Question 64

64. 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

Answer 94

None of these

Answer 95

x² + (α + β)x + αβ = 0

Answer 96

x² - (α + β)x - αβ = 0

Answer 97

x² + (α + β)x - αβ = 0

Answer 98

x² - (α + β)x + αβ = 0

Answer 99

None of these

Answer 100

Polynomial

Answer 101

ab² – bx + c = 0

Answer 102

x² – bx + ac

Answer 103

abx² – x + ac² = 0

Answer 104

abx² – b²x + ac² = 0

Answer 105

Exactly four roots

Answer 106

Infinitely many roots

Answer 107

Exactly two roots

Answer 108

Natural numbers

Answer 109

Rational number

Answer 110

None of these

Answer 111

x² – 6x + 11 = 0

Answer 112

3x² – 2x + 1 = 0

Answer 113

x² – 11x + 6 = 0

Answer 114

x² – 6x – 11

Answer 115

1/α, 1/β

Answer 116

x² + 4x + 1 = 0

Answer 117

x² - 4x + 1 = 0

Answer 118

x² - 6x – 6 = 0

Answer 119

x² - 6x + 6 = 0

Answer 120

x² – Sx – P = 0

Answer 121

x² + Sx + P = 0

Answer 122

x² + Sx – P = 0

Answer 123

x² – Sx + P = 0

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

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