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ECAT Mathematics Quadratic Equations Online Test

Maan AliLast Updated: April 18, 2025

Mathematics Quadratic Equations MCQS Online Test

ECAT Math Quadratic Equations Chapter Online Test

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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ECAT Math Quadratic Equations MCQS Online Test

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Page 1 of 4

Math

1. Which one is true?

w³ = 1

w² = 1/w

w = 1/w²

All

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

None of these

25/4

± 25/4

25/5

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

b = 0, c = 0

a = b = c = 0

b = 0

c = 0

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

5, 5 ω, 5 ω²

-3, -3 ω, -3 ω²

-5, -5 ω, -5 ω²

3,3 ω, 3 ω²

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

n/p

t/p

-t/p

None of these

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

Radical

Quadratic

Reciprocal

Exponential

7. x³ – 3x² + 2x – 6 has a factor

x – 4

x + 3

x – 3

x + 2

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

a < 0

a > 0

a ≠ 0, b ≠ 0

a ≠ 0

9. The quadratic equation whose roots are α β is

x² + (α + β)x + αβ = 0

x² - (α + β)x - αβ = 0

x² + (α + β)x - αβ = 0

x² - (α + β)x + αβ = 0

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

[3, 4]

(-9, 4)

(3, 4)

[9, 3]

11. 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

(2, ∞)

(-∞, -1)

(-1, -4/5)

(4/5, 2)

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

-5/9

-3

-1/3

5/27

13. Two square roots of the unity are

t, t²

1, - ω

-1, ω

1, -1

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

a = 2

a = 0

a = – 3

a = – 2

15. x² + 4x + 4 is

Polynomial

Equation

None of these

Identity

16. 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

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

α,1/β

1/α, 1/β

β, 1/α

- α,- β

18. 1+w+w² = ?

None of these

-1

19. A polynomial having one term is called

Binomial

None of these

Monomial

Trinomial

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

Polynomial of degree n

Polynomial of degree 0

Polynomial of degree 3

Polynomial of degree 2

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

x = - a/2b

x = - b/2a

x = a/2b

None of these

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

2 + i

- i

2 - i

23. 3x² + 2x + 1 is a

Polynomial of degree 3

Polynomial of degree n

Polynomial of degree 0

Polynomial of degree 2

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

-c/a

-b/a

c/a

b/a

25. Quadratic equation is an equation of degree

Page 2 of 4

26. 7y2 + 5 √y + 3 is a polynomial over

Rational number

None of these

Integers

Natural numbers

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

Reciprocal

Rational

None of these

Irrational

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

None of these

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

b/a

c/a

- b/a

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

Real & unequal

Complex

Irrational

Real & equal

31. 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.

a – b/a + b

b – c/b + c

c – a/c + a

None of these

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

27/16

None of these

16/27

- 27/16

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

None of these

b/a

-b/a

c/a

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

α = β

αβ = 1

α = 1

β = α

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

x² – 6x + 11 = 0

x² – 6x – 11

3x² – 2x + 1 = 0

x² – 11x + 6 = 0

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

Infinitely many roots

Exactly two roots

Exactly four roots

No roots

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

>0 and is a perfect square

38. The four fourth roots of unity are

-4, 4, -4i, 4i

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

-3, 3, -3i, 3i

-1,1, -i, i

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

x² - 4x + 1 = 0

x² - 6x + 6 = 0

x² + 4x + 1 = 0

x² - 6x – 6 = 0

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

1, 8

2, 8

2, 3

1, 3

41. 3x⁴ + √5 x² + 3x + 1 is a polynomial of degree

42. 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:

x² – Sx + P = 0

x² – Sx – P = 0

x² + Sx – P = 0

x² + Sx + P = 0

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

a = 7

a = –7

a = 0

a = 1

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

2ω

ω²

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

a = 0

a = -7

a = 1

a = 7

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

f(1/a)

f(–1/a)

f(a)

f(–a)

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

x² + Sx – P = 0

x² – Sx – P = 0

x² + Sx + P = 0

x² – Sx + P = 0

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

Non-real with negative real parts

Real and negative

Real and positive

Nothing can be said

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

Real

Depends upon b

Depends upon a

Depends upon a and b

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

b = 0

d = 0

b = c

a = c

Page 3 of 4

51. 3 x 2 + 2x + 1 is a

Polynomial of degree n

Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 0

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

±12

-12

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

b² – 4ac > 0

b² – 4ac = 0

None of these

b² – 4ac < 0

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

–5, – 30

–5, 30

None of these

5, 30

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

None of these

Reciprocal

Rational

Irrational

56. 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

Q(x) = (x – r)P (x) + R

P(x) = (x – r)R + Q(x)

P(x) = (x – r)Q (x) + R

Q(x) = (x – r)R + P(x)

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

p² + 4q = 0

p² - 4p = 0

q² + 4p = 0

q² - 4p = 0

58. Cube roots of -64 are

4, 4w, 4w²

-4, -4w, -4w²

4, w, w²

-4, w, w²

59. w¹⁰⁹ = ?

[-1-√3/2]

[-1+i√3/2]

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

f(0)

f(-a)

f(a)

-af(a)

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

14x²

-32x²

30x²

3x²

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

None of these

Positive

Negative

Real

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

{-23, 19}

{-2, 9}

{2, -9}

{23, -19}

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

b = 0

None of these

a = 0

c = 0

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

-18

-9

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

-35/16

-9

35/16

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

-2

-1

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

Imaginary

Real

Irrational

Equal

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

d² – 4ce

None of these

d + 4ce

4ce

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

a > 0, b > 0

a = 0

ab > 0

ab < 0

71. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

-2

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

abx² – b²x + ac² = 0

x² – bx + ac

ab² – bx + c = 0

abx² – x + ac² = 0

73. The first degree function are called function

Quadratic

Linear

None of these

Cubic

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

x = -1, x = 6

x = 6

x = 1

x = 1, x = -6

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

2a³

a³

-a³

Page 4 of 4

76. The quadratic formula is

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

c = 0, b ≠ 0

b = 0, c ≠ 0

b = 0, c = 0

c = 0

78. The polynomial ax³ + bx² + 8 has degree

None of these

a + b

Physics

79. The graph of the quadratic function is

Circle

Rectangle

Triangle

Parabola

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Maan AliLast Updated: April 18, 2025

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ECAT Mathematics Quadratic Equations Online Test

Mathematics Quadratic Equations MCQS Online Test

ECAT Math Quadratic Equations Chapter Online Test

ECAT Math Quadratic Equations MCQS Online Test

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