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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
The condition for ax2 + bx c to be expressed as the product of linear polynomials is
Choose an answer
b4 - 4ac =0
b4- 4ac ≥0
b4- 4ac <0
b4= 4ac
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Question # 2
If 2x
1/3
+ 2x
-1/3
= 5, then x is equal to
Choose an answer
1 or -1
2 or 1/2
8 or 1/8
4 or 1/4
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Question # 3
4
1+x
+ 4
1-x
= 10 is called
Choose an answer
Reciprocal equation
Exponential equation
Radical equation
None of these
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Question # 4
For any integer k, w
n
= ______ when n = 3k
Choose an answer
1
2
0
-4
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Question # 5
If a parabola opens down, then its vertex is at the
Choose an answer
Right of the parabola
Left of parabola
Lowest point on the parabola
Highest point on the parabola
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Question # 6
The roots of the equation ax
2
+ bx + c = 0 are real and equal if
Choose an answer
b
2
- 4ac < 0
b
2
- 4ac = 0
b
2
- 4ac > 0
None of these
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Question # 7
(1+w)(1+w2)(1+w4)(1+w8)....50 factors
Choose an answer
0
-1
1
2
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Question # 8
Choose an answer
0
1
2
None of these
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Question # 9
If one root of the equation ix
2
- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is
Choose an answer
-i
2 + i
i
2 - i
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Question # 10
Choose an answer
-1
0
2
1
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Question # 11
The roots of ax2 + bx + c = 0 are always unequal if
Choose an answer
b2 - 4ac = 0
b2- 4ac ≠ 0
b2- 4ac > 0
b2- 4ac ≥ 0
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Question # 12
The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0
Choose an answer
4
64
8
All values of k
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Question # 13
The standard form of the quadratic function f(x) = -x
2
+4x+2, is
Choose an answer
(x-2)
2
+6
-(x-2)
2
+ 6
(x-3)
2
+5
(x+4)
2
-7
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Question # 14
If x-2 and x-1 both are factors of x
3
-3x
3
+2x-4p, then P must equal to
Choose an answer
1
2
0
-2
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Question # 15
If the roots of ax
2
+ bx + c = 0 (a > 0) be greater than unity, then
Choose an answer
a + b + c = 0
a + b + c > 0
a + b + c < 0
None of these
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Question # 16
If the roots of ax
2
+ b = 0 are real and distinct then
Choose an answer
ab > 0
a = 0
ab < 0
a > 0, b > 0
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Question # 17
The roots of the equations will be equal if b
2
- 4ac is
Choose an answer
Positive
Negative
1
Zero
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Question # 18
The sum of the roots of the equation x2 -6x +2 = 0 is
Choose an answer
-6
2
-2
6
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Question # 19
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 # 20
w
-12
= ______
Choose an answer
0
1
w
w
2
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Question # 21
Choose an answer
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Question # 22
Find a if 1 is a root of the equation x
2
+ ax + 2 = 0
Choose an answer
3
-3
2
0
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Question # 23
Choose an answer
(-1, 2)
(-1, 1)
(1, 2)
{-1}
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Question # 24
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 # 25
The standard parabolic form of the equation f(x) = x
2
+4 x +1 is
Choose an answer
x(x+4)+1
(x+2)
2
-3
(x+4)
3
+ 9
x(x-2)
2
+1
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Question # 26
The roots of px2 - (p-q)x-q=0 are
Choose an answer
equal
Irrational
Rational
Imaginary
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Question # 27
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Question # 28
A polynomial of arbitrary degree
Choose an answer
f(x) = o
f(x) = x
f(x) = a
f(x) = ax + b,a ≠ 0
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Question # 29
w
-1
= ______
Choose an answer
0
1
w
w
2
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Question # 30
Choose an answer
c/a
-c/a
b/a
-b/a
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Question # 31
If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are
Choose an answer
Real and negative
Non-real with negative real parts
Real and positive
Nothing can be said
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