Mathematics Quadratic Equations Online Mcqs Test

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Question 1

1. 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 2

2. 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 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

Q(x) = (x – r)P (x) + R

Answer

P(x) = (x – r)R + Q(x)

Answer

Q(x) = (x – r)R + P(x)

Question 4

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

Answer

None of these

Answer

Irrational

Answer

Reciprocal

Question 5

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

Answer

Irrational

Answer

Real & equal

Answer

Real & unequal

Question 6

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

Question 7

7. 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 8

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

Answer

Reciprocal

Answer

Irrational

Answer

None of these

Question 9

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

Answer

a = b = c = 0

Answer

b = 0, c = 0

Question 10

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

Question 11

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

Question 12

12. Which one is true?

Question 13

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

Question 14

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

Answer

Exponential

Answer

Reciprocal

Question 15

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

Answer

None of these

Question 16

16. 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 17

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

Answer

a > 0, b > 0

Question 18

18. 3x² + 2x + 1 is a

Answer

Polynomial of degree n

Answer

Polynomial of degree 0

Answer

Polynomial of degree 2

Answer

Polynomial of degree 3

Question 19

19. 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 20

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

Question 21

21. 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 22

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

Answer

Polynomial of degree 0

Answer

Polynomial of degree n

Answer

Polynomial of degree 3

Answer

Polynomial of degree 2

Question 23

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

Answer

Depends upon a

Answer

Depends upon a and b

Answer

Depends upon b

Question 24

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

Question 25

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

Answer

None of these

Question 26

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

Answer

None of these

Question 27

27. The quadratic formula is

Question 28

28. The polynomial ax³ + bx² + 8 has degree

Answer

None of these

Question 29

29. 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 30

30. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

Question 31

31. 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 32

32. 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 33

33. Quadratic equation is an equation of degree

Question 34

34. Cube roots of -64 are

Answer

4, 4w, 4w²

Answer

-4, w, w²

Answer

-4, -4w, -4w²

Question 35

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

Question 36

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

Answer

>0 and is a perfect square

Question 37

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

Answer

Exactly four roots

Answer

Infinitely many roots

Answer

Exactly two roots

Question 38

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

Question 39

39. Two square roots of the unity are

Question 40

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

Question 41

41. x² + 4x + 4 is

Answer

None of these

Answer

Polynomial

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

Question 44

44. 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 45

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

Question 46

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

Answer

None of these

Question 47

47. w¹⁰⁹ = ?

Answer

[-1+i√3/2]

Answer

[-1-√3/2]

Question 48

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

Question 49

49. 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 50

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

Question 51

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

Question 52

52. A polynomial having one term is called

Answer

None of these

Question 53

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

Answer

None of these

Question 54

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

Question 55

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

Question 56

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

Question 57

57. 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 58

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

Answer

Irrational

Question 59

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

Question 60

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

Question 61

61. 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 62

62. 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 63

63. 1+w+w² = ?

Answer

None of these

Question 64

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

Answer

q² + 4p = 0

Answer

p² - 4p = 0

Answer

p² + 4q = 0

Answer

q² - 4p = 0

Answer 99

None of these

Answer 100

Rational number

Answer 101

Natural numbers

Answer 102

None of these

Answer 103

None of these

Answer 104

Polynomial of degree 0

Answer 105

Polynomial of degree 3

Answer 106

Polynomial of degree n

Answer 107

Polynomial of degree 2

Answer 108

None of these

Answer 109

x² – 11x + 6 = 0

Answer 110

3x² – 2x + 1 = 0

Answer 111

x² – 6x + 11 = 0

Answer 112

x² – 6x – 11

Answer 113

a – b/a + b

Answer 114

b – c/b + c

Answer 115

None of these

Answer 116

c – a/c + a

Answer 117

x = 1, x = -6

Answer 118

x = -1, x = 6

Answer 119

-3, 3, -3i, 3i

Answer 120

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

Answer 121

-1,1, -i, i

Answer 122

-4, 4, -4i, 4i

Answer 123

a ≠ 0, b ≠ 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

Math Quadratic Equations Practice Test Online With Explanation

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