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

Answer

Irrational

Question 2

2. Cube roots of -64 are

Answer

-4, -4w, -4w²

Answer

4, 4w, 4w²

Answer

-4, w, w²

Question 3

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

Answer

None of these

Question 4

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

Question 5

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

Answer

None of these

Question 6

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

Answer

None of these

Question 7

7. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

Question 8

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

Answer

Exponential

Answer

Reciprocal

Question 9

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

Answer

None of these

Question 10

10. A polynomial having one term is called

Answer

None of these

Question 11

11. 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 12

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

Question 13

13. x² + 4x + 4 is

Answer

None of these

Answer

Polynomial

Question 14

14. 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 15

15. 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 16

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

Answer

x² - 6x – 6 = 0

Answer

x² - 6x + 6 = 0

Answer

x² - 4x + 1 = 0

Answer

x² + 4x + 1 = 0

Question 17

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

Answer

a ≠ 0, b ≠ 0

Question 18

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

Answer

None of these

Answer

x = - b/2a

Answer

x = - a/2b

Question 19

19. 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 20

20. 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

c – a/c + a

Answer

a – b/a + b

Answer

None of these

Answer

b – c/b + c

Question 21

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

Question 22

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

Answer

3x² – 2x + 1 = 0

Answer

x² – 11x + 6 = 0

Answer

x² – 6x + 11 = 0

Answer

x² – 6x – 11

Question 23

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

Question 24

24. Which one is true?

Question 25

25. x³ – 3x² + 2x – 6 has a factor

Question 26

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

Question 27

27. If x² + 6x – 27 > 0 and – x² + 3x + 4 > 0, the x lies in the interval.

Question 28

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

Answer

Polynomial of degree 2

Answer

Polynomial of degree 3

Answer

Polynomial of degree 0

Answer

Polynomial of degree n

Question 29

29. Two square roots of the unity are

Question 30

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

Answer

Reciprocal

Answer

None of these

Answer

Irrational

Question 31

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

Answer

b = 0, c = 0

Answer

a = b = c = 0

Question 32

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

Question 33

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

Answer

>0 and is a perfect square

Question 34

34. 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 35

35. The first degree function are called function

Answer

None of these

Question 36

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

Question 37

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

Answer

Irrational

Answer

Reciprocal

Answer

None of these

Question 38

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

Answer

c = 0, b ≠ 0

Answer

b = 0, c ≠ 0

Answer

b = 0, c = 0

Question 39

39. 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)R + P(x)

Answer

P(x) = (x – r)R + Q(x)

Answer

Q(x) = (x – r)P (x) + R

Question 40

40. 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

-3, -3 ω, -3 ω²

Answer

-5, -5 ω, -5 ω²

Question 41

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

Answer

a > 0, b > 0

Question 42

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

Answer

Exactly two roots

Answer

Exactly four roots

Answer

Infinitely many roots

Question 43

43. Quadratic equation is an equation of degree

Question 44

44. 1+w+w² = ?

Answer

None of these

Question 45

45. 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 46

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

Question 47

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

Question 48

48. 3x⁴ + √5 x² + 3x + 1 is a polynomial of degree

Question 49

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

Answer

x² – bx + ac

Answer

abx² – x + ac² = 0

Answer

ab² – bx + c = 0

Answer

abx² – b²x + ac² = 0

Question 50

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

Answer

None of these

Question 51

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

Question 52

52. 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 53

53. w¹⁰⁹ = ?

Answer

[-1-√3/2]

Answer

[-1+i√3/2]

Question 54

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

Question 55

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

Question 56

56. 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 57

57. 3x² + 2x + 1 is a

Answer

Polynomial of degree 0

Answer

Polynomial of degree 3

Answer

Polynomial of degree 2

Answer

Polynomial of degree n

Question 58

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

Question 59

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

Answer

Real and positive

Answer

Non-real with negative real parts

Answer

Nothing can be said

Answer

Real and negative

Question 60

60. 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 61

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

Answer

Real & equal

Answer

Irrational

Answer

Real & unequal

Question 62

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

Answer

None of these

Answer

b² – 4ac = 0

Answer

b² – 4ac < 0

Answer

b² – 4ac > 0

Question 63

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

Question 64

64. The quadratic formula is

Answer 102

Depends upon b

Answer 103

Depends upon a

Answer 104

Depends upon a and b

Answer 105

x² – Sx – P = 0

Answer 106

x² + Sx – P = 0

Answer 107

x² – Sx + P = 0

Answer 108

x² + Sx + P = 0

Answer 109

None of these

Answer 110

Natural numbers

Answer 111

None of these

Answer 112

Rational number

Answer 113

x = -1, x = 6

Answer 114

x = 1, x = -6

Answer 115

q² + 4p = 0

Answer 116

p² - 4p = 0

Answer 117

q² - 4p = 0

Answer 118

p² + 4q = 0

Answer 119

Polynomial of degree 0

Answer 120

Polynomial of degree 2

Answer 121

Polynomial of degree 3

Answer 122

Polynomial of degree n

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

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