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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
Choose an answer
Only one real solution
Exactly three real solution
Exactly one rational solution
Non-real roots
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Question # 2
If a (p + q)
2
+ bpq +c = 0 and a (p + r)
2
+ 2 bpr + c = 0, then qr equals
Choose an answer
p
2
+ c/a
p
2
+ a/c
p
2
+ c/a
p
2
- c/a
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Question # 3
Choose an answer
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Question # 4
Choose an answer
1
-1
5
2
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Question # 5
(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if
Choose an answer
a+b=c+d
a+c=b+d
a+d=b+c
All are correct
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Question # 6
Choose an answer
0
-1-w
2
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Question # 7
The roots of ax2+bx+c=0 are
Choose an answer
Rational ⇔ b2 -4 ac ≥ 0
Irrational ⇔ b2-4 ac > 0
Real ⇔ b2-4 ac ≠ 0
Rational⇔ b2-4 ac = 0
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Question # 8
Roots of the equation x
2
- x = 2 are
Choose an answer
{2, -1}
{1, 0}
{2, 1}
{-2, 1}
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Question # 9
w
29
= ______
Choose an answer
0
1
w
w
2
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Question # 10
The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is
Choose an answer
a > 0
a < 0
a≠ 0
a≠ 0,b ≠ 0
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Question # 11
The quadratic formula is
Choose an answer
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Question # 12
Two quadratic equation in which xy term is missing and the coefficients of x
2
and y
2
are equal, give a linear equation by ______
Choose an answer
Addition
Subtraction
Multiplication
Division
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Question # 13
Choose an answer
15
9
7
8
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Question # 14
Choose an answer
-1
0
2
1
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Question # 15
The equation (cos p - 1)x
2
+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval
Choose an answer
(0, 2
π
)
(-
π
, -0)
(0,
π
)
None of these
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Question # 16
If w is a cube root of unity then 1 + w + w
2
= ______
Choose an answer
1
2
0
-1
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Question # 17
Roots of the equation x
2
+ 2x + 3 = 0 are
Choose an answer
Real and equal
Real and distinct
Complex
None of these
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Question # 18
If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______
Choose an answer
-5
5
0
1
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Question # 19
(2 + w) (2 + w
2
) = ______
Choose an answer
1
2
3
0
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Question # 20
Choose an answer
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Question # 21
The set of real roots of the equation log
(5x + 4)
(2x +3)
3
- log
(2x + 3)
(10x
2
+ 23x + 12) = 1 is
Choose an answer
{-1}
{-3/5}
Empty set
{-1/3}
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Question # 22
The roots of the equation ax
2
+ bx + c = 0 are complex/imaginary if
Choose an answer
b
2
- 4ac < 0
b
2
- 4ac = 0
b
2
- 4ac > 0
None of these
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Question # 23
If 3x
4
+ 4x
3
+ x - 5 is divided by x + 1, then the reminder is
Choose an answer
0
7
-7
5
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Question # 24
w
4
= ______
Choose an answer
0
1
w
w
2
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