Mathematics Quadratic Equations Online Mcqs Test

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Question 1

1. 3x² + 2x + 1 is a

Answer

Polynomial of degree 2

Answer

Polynomial of degree 0

Answer

Polynomial of degree n

Answer

Polynomial of degree 3

Question 2

2. The four fourth roots of unity are

Answer

-1,1, -i, i

Answer

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

Answer

-4, 4, -4i, 4i

Answer

-3, 3, -3i, 3i

Question 3

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

Answer

p² + 4q = 0

Answer

p² - 4p = 0

Answer

q² + 4p = 0

Answer

q² - 4p = 0

Question 4

4. 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 5

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

Answer

a > 0, b > 0

Question 6

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

Answer

x² – 11x + 6 = 0

Answer

x² – 6x + 11 = 0

Answer

x² – 6x – 11

Answer

3x² – 2x + 1 = 0

Question 7

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

Question 8

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

Question 9

9. 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 10

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

Answer

a ≠ 0, b ≠ 0

Question 11

11. 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

None of these

Answer

a – b/a + b

Answer

c – a/c + a

Question 12

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

Question 13

13. The first degree function are called function

Answer

None of these

Question 14

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

Answer

None of these

Question 15

15. 3x⁴ + √5 x² + 3x + 1 is a polynomial of degree

Question 16

16. A polynomial having one term is called

Answer

None of these

Question 17

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

Question 18

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

Question 19

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

Answer

Real & equal

Answer

Irrational

Answer

Real & unequal

Question 20

20. Quadratic equation is an equation of degree

Question 21

21. 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

Q(x) = (x – r)R + P(x)

Answer

Q(x) = (x – r)P (x) + R

Answer

P(x) = (x – r)R + Q(x)

Answer

P(x) = (x – r)Q (x) + R

Question 22

22. 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 23

23. 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 24

24. 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 25

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

Question 26

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

Question 27

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

Answer

Depends upon a and b

Answer

Depends upon a

Answer

Depends upon b

Question 28

28. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

Question 29

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

Answer

None of these

Question 30

30. Which one is true?

Question 31

31. The polynomial ax³ + bx² + 8 has degree

Answer

None of these

Question 32

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

Answer

Irrational

Question 33

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

Answer

None of these

Question 34

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

Answer

None of these

Question 35

35. 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

-5, -5 ω, -5 ω²

Answer

3,3 ω, 3 ω²

Question 36

36. 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 37

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

Answer

Reciprocal

Answer

Irrational

Answer

None of these

Question 38

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

Answer

a = b = c = 0

Answer

b = 0, c = 0

Question 39

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

Question 40

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

Answer

None of these

Question 41

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

Question 42

42. x³ – 3x² + 2x – 6 has a factor

Question 43

43. Two square roots of the unity are

Question 44

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

Answer

abx² – x + ac² = 0

Answer

abx² – b²x + ac² = 0

Answer

ab² – bx + c = 0

Answer

x² – bx + ac

Question 45

45. x² + 4x + 4 is

Answer

Polynomial

Answer

None of these

Question 46

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

Question 47

47. Cube roots of -64 are

Answer

-4, w, w²

Answer

-4, -4w, -4w²

Answer

4, 4w, 4w²

Question 48

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

Question 49

49. 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 50

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

Answer

Exactly two roots

Answer

Infinitely many roots

Answer

Exactly four roots

Question 51

51. 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 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. 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 54

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

Answer

Nothing can be said

Answer

Non-real with negative real parts

Answer

Real and negative

Answer

Real and positive

Question 55

55. w¹⁰⁹ = ?

Answer

[-1-√3/2]

Answer

[-1+i√3/2]

Question 56

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

Answer

Reciprocal

Answer

Exponential

Question 57

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

Question 58

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

Answer

None of these

Question 59

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

Question 60

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

Answer

>0 and is a perfect square

Question 61

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

Answer

x = 1, x = -6

Answer

x = -1, x = 6

Question 62

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

Question 63

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

Answer

x² - 6x + 6 = 0

Answer

x² - 4x + 1 = 0

Answer

x² - 6x – 6 = 0

Answer

x² + 4x + 1 = 0

Question 64

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

Answer

b = 0, c ≠ 0

Answer

c = 0, b ≠ 0

Answer

b = 0, c = 0

Answer 107

Polynomial of degree 0

Answer 108

Polynomial of degree 2

Answer 109

Polynomial of degree 3

Answer 110

Polynomial of degree n

Answer 111

None of these

Answer 112

d² – 4ce

Answer 113

None of these

Answer 114

None of these

Answer 115

Natural numbers

Answer 116

Rational number

Answer 117

None of these

Answer 118

Reciprocal

Answer 119

Irrational

Answer 120

Polynomial of degree 2

Answer 121

Polynomial of degree 0

Answer 122

Polynomial of degree n

Answer 123

Polynomial of degree 3

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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