Home/ECAT/ECAT Mathematics Quadratic Equations Online Test

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.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

ECAT Math Quadratic Equations MCQS Online Test

Page 1 of 4

Math

1. 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

x² – 11x + 6 = 0

x² – 6x + 11 = 0

3x² – 2x + 1 = 0

2. 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.

None of these

a – b/a + b

c – a/c + a

b – c/b + c

3. 1+w+w² = ?

-1

None of these

4. 3x² + 2x + 1 is a

Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree n

Polynomial of degree 0

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

-3

5/27

-1/3

-5/9

6. 7y2 + 5 √y + 3 is a polynomial over

Integers

Rational number

Natural numbers

None of these

7. x² + 4x + 4 is

Polynomial

Equation

Identity

None of these

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

a ≠ 0

a > 0

a < 0

a ≠ 0, b ≠ 0

9. The quadratic formula is

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

a = – 3

a = 0

a = – 2

a = 2

11. The first degree function are called function

None of these

Cubic

Linear

Quadratic

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

Rational

Reciprocal

None of these

Irrational

13. A polynomial having one term is called

Monomial

Trinomial

None of these

Binomial

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

x² - 6x + 6 = 0

x² - 4x + 1 = 0

x² - 6x – 6 = 0

x² + 4x + 1 = 0

15. 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

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

a = 0

ab < 0

a > 0, b > 0

ab > 0

17. The four fourth roots of unity are

-4, 4, -4i, 4i

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

-3, 3, -3i, 3i

-1,1, -i, i

18. 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

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

±12

-12

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

-18

-9

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

Q(x) = (x – r)P (x) + R

Q(x) = (x – r)R + P(x)

P(x) = (x – r)R + Q(x)

P(x) = (x – r)Q (x) + R

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

None of these

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

2ω

ω²

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

β, 1/α

- α,- β

α,1/β

1/α, 1/β

25. x³ – 3x² + 2x – 6 has a factor

x – 4

x – 3

x + 2

x + 3

Page 2 of 4

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

-b/a

b/a

-c/a

c/a

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

None of these

c/a

-b/a

b/a

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

q² - 4p = 0

p² - 4p = 0

q² + 4p = 0

p² + 4q = 0

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

a = 1

a = 7

a = 0

a = –7

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

{-2, 9}

{-23, 19}

{2, -9}

{23, -19}

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

b = 0

b = c

a = c

d = 0

32. 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

33. Two square roots of the unity are

-1, ω

1, -1

t, t²

1, - ω

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

x = 6

x = -1, x = 6

x = 1, x = -6

x = 1

35. 3x⁴ + √5 x² + 3x + 1 is a polynomial of degree

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

a = 1

a = 0

a = -7

a = 7

37. [1 + √-3/2]⁹ + [1 - √-3/2]⁹ = ?

-2

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

x² – bx + ac

abx² – x + ac² = 0

ab² – bx + c = 0

abx² – b²x + ac² = 0

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

f(a)

f(–a)

f(–1/a)

f(1/a)

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

Real

Imaginary

Irrational

Equal

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

b² – 4ac > 0

None of these

b² – 4ac < 0

b² – 4ac = 0

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

Real

Depends upon a

Depends upon a and b

Depends upon b

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

-2

-1

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

27/16

- 27/16

None of these

16/27

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

c = 0

None of these

b = 0

a = 0

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

b = 0, c = 0

a = b = c = 0

c = 0

b = 0

47. w¹⁰⁹ = ?

[-1+i√3/2]

[-1-√3/2]

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

Real

Positive

None of these

Negative

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

n/p

-t/p

None of these

t/p

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

Reciprocal

None of these

Rational

Irrational

Page 3 of 4

51. 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

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

Real & equal

Irrational

Complex

Real & unequal

53. 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

-3, -3 ω, -3 ω²

-5, -5 ω, -5 ω²

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

Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree n

Polynomial of degree 0

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

αβ = 1

α = 1

α = β

β = α

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

Exponential

Radical

Reciprocal

Quadratic

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

(3, 4)

(-9, 4)

[9, 3]

[3, 4]

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

d + 4ce

None of these

4ce

d² – 4ce

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

Exactly two roots

No roots

Exactly four roots

Infinitely many roots

60. 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

(-1, -4/5)

(-∞, -1)

(4/5, 2)

(2, ∞)

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

None of these

25/5

25/4

± 25/4

62. Cube roots of -64 are

4, 4w, 4w²

4, w, w²

-4, w, w²

-4, -4w, -4w²

63. Which one is true?

All

w³ = 1

w = 1/w²

w² = 1/w

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

x = - a/2b

x = - b/2a

None of these

x = a/2b

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

None of these

5, 30

–5, 30

–5, – 30

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

- i

2 + i

2 - i

67. 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 positive

Real and negative

Nothing can be said

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

-35/16

35/16

-9

69. 3 x 2 + 2x + 1 is a

Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 0

Polynomial of degree n

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

>0 and is a perfect square

71. The polynomial ax³ + bx² + 8 has degree

None of these

a + b

72. Quadratic equation is an equation of degree

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

f(a)

-af(a)

f(-a)

f(0)

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

- b/a

c/a

b/a

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

3x²

30x²

-32x²

14x²

Page 4 of 4

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

-a³

a³

2a³

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

2, 8

2, 3

1, 3

1, 8

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

b = 0, c ≠ 0

c = 0

b = 0, c = 0

c = 0, b ≠ 0

Physics

79. The graph of the quadratic function is

Rectangle

Triangle

Circle

Parabola

You Can Learn and Gain more Knowledge through our Online Quiz and Testing system Just Search your desired Preparation subject at Gotest.

ECAT Chemistry Environmental Chemistry Test Online
ECAT Chemistry Common Chemical Industries in Pakistan Test O...
ECAT Chemistry Macro-Molecules Test Online
ECAT Chemistry Carboxylic Acid Test Online
ECAT Chemistry Aldehydes and Ketones Test Online
ECAT Chemistry Alcohols Phenols And Ethers Test Online
ECAT Chemistry Alkyl Halides Test Online
ECAT Chemistry Aromatic Hydrocarbons Test Online
ECAT Chemistry Aliphatic Hydrocarbons Test Online
ECAT Chemistry Fundamental Principles of Organic Chemistry T...

Maan AliLast Updated: April 18, 2025

Facebook Twitter Reddit WhatsApp Share via Email Print

13 Comments

Khudabux mari IbA college Nausharoferoze says:

June 2, 2022 at 9:12 am

72

Khudabux mari IbA college Nausharoferoze says:

June 2, 2022 at 9:07 am

64

Sakim ullah khan says:

January 9, 2022 at 3:37 am

I apply for the post of pst ,CT and how can I prepare for our self study to pass with high marks

AWAIS ALI says:

August 8, 2020 at 11:06 am

i got 80%

Hamza says:

July 26, 2020 at 6:11 pm

84%

faisal shami says:

July 13, 2017 at 1:42 pm

Ecat preparation

1. Muhammad Awais says:
  
  August 14, 2022 at 3:14 am
  
  Required my answers
  
Abdul SAmmad Butt says:

July 12, 2017 at 12:14 pm

80%

Fatima says:

July 10, 2017 at 3:14 pm

84%

Ayesha Muhammad says:

May 10, 2017 at 9:36 pm

Could anyone guide me for the Iba (institute of business administration) test . I want to give an attempt this July . Where should I prep from

1. izhan says:
  
  November 21, 2018 at 7:34 pm
  
  you can come to my home for prep
  
2. Qayyum Malik says:
  
  July 16, 2020 at 12:51 pm
  
  Yes you can contact with me.i will guide you about all info you want.I will add you in a group where you will get best of the knowledge.03023248350 and 03048153918
  
tufail ahmed says:

October 4, 2016 at 1:07 pm

80%

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

Math

Physics

You Might Also Like

Maan Ali

13 Comments

Leave a Reply Cancel reply

Mathematics Quadratic Equations MCQS Online Test

ECAT Math Quadratic Equations Chapter Online Test

ECAT Math Quadratic Equations MCQS Online Test

Math

Physics

You Might Also Like

Maan Ali

Your Related

ECAT Chemistry Common Chemical Industries in Pakistan Test Online

ECAT Chemistry Transition Elements Test Online

ECAT Mathematics Differentiation Online Test

ECAT Physics Oscillations Test Online

ECAT Mathematics Matrices and Determinants Online Test

ECAT Chemistry Forms of Matter Test Online

13 Comments

Leave a Reply Cancel reply