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ECAT Pre General Science Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
The roots of (x - a)(x - b) = ab x2 are always
Choose an answer
Real
Depends upon a
Depends upon b
Depends upon a and b
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Question # 2
The solution set of x
2
- 5x + 6 = 0 is
Choose an answer
{1, 3}
{2, 3}
{1, 2}
None of these
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Question # 3
Choose an answer
Polynomial of degree 0
Polynomial of degree 1
Polynomial of degree 2
Polynomial of degree n
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Question # 4
The solution of equation x2 + 2 = 0 in the set of real number is
Choose an answer
Infinite set
Singleton set
Null set
None of these
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Question # 5
If a polynomial p(x) is divided by x-c, then the remainder is
Choose an answer
p(x)
x-c
c
P(c)
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Question # 6
w
11
= ______
Choose an answer
0
1
w
w
2
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Question # 7
Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then
Choose an answer
α = β
αβ = 1
α = β
α = 1
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Question # 8
If sin
α
and cos
α
are the roots of the equation px
2
+ qx + r =0, then
Choose an answer
p
2
- q
2
+ 2pr = 0
(p + r)
2
= q
2
- r
2
p
2
+ q
2
- 2pr = 0
(p - r)
2
= q
2
+ r
2
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Question # 9
Choose an answer
1
-1
5
2
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Question # 10
If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then
Choose an answer
k=0
k=1
k=w
k=w2
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Question # 11
Choose an answer
0
1
2
None of these
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Question # 12
If the roots of 3x2+kx + 12 = 0 are equal then k = ______
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Question # 13
Choose an answer
(-1, 2)
(-1, 1)
(1, 2)
{-1}
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Question # 14
If ax + bx + c =0 is satisfied by every value of x,then
Choose an answer
b = 0,c = 0
c = 0
b = 0
a = b = c = 0
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Question # 15
There are ______ basic techniques for solving a quadratic equation
Choose an answer
Two
Three
Four
None of these
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Question # 16
If one root of the equation x
2
- 3x + a = 0 is 2 then a = ______
Choose an answer
0
1
2
3
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Question # 17
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 # 18
if one root of the equation ix2 - 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 # 19
In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are
Choose an answer
6, 10
-6, -10
8, 8
-8, -8
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Question # 20
w
15
= ______
Choose an answer
0
1
w
w
2
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Question # 21
Choose an answer
Polynomial of degree 0
Polynomial of degree 2
Quadratic equation
None of these
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Question # 22
For the equation |x
2
| + |x| -6 =0, the roots are
Choose an answer
One and only one real number
Real with sum one
Real with sum zero
Real with product zero
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Question # 23
Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always
Choose an answer
Positive
Negative
Real
None of these
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Question # 24
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 # 25
Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always
Choose an answer
Positive
Negative
Real
None of these
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Question # 26
If the roots of ax
2
- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is
Choose an answer
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Question # 27
If b
2
- 4ac = 0 then the roots of the equation are
Choose an answer
Real and distinct
Real and equal
Imaginary
None of these
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Question # 28
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 # 29
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 # 30
w
4
= ______
Choose an answer
0
1
w
w
2
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Question # 31
The roots of the equation will be irrational if b
2
- 4ac is
Choose an answer
Positive and perfect square
Positive but not a perfect square
Negative
Zero
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