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ECAT Pre General Science Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
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 # 2
Choose an answer
1
2
0
4
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Question # 3
Root of the equation 3
x-1
+ 3
1-x
= is
Choose an answer
2
1
0
-1
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Question # 4
In quadratic equation f(x) = ax
2
,if a >0, then the graph of parabola
Choose an answer
Opens up
Opens down
close up
symmetric w.r.t.x.axis
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Question # 5
Each complex cube root of unity is square of
Choose an answer
itself
1
-1
the other
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Question # 6
The quadratic equation 8 sec
2
θ
- 6 sec
θ
+1 = 0 has
Choose an answer
Infinitely many roots
Exactly two roots
Exactly four roots
No roots
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Question # 7
If f(x) = ax
2
, and a>0, then the lowest point on the parabola is called.
Choose an answer
Vertex of parabola
Co-ordinates of parabola
Roots of the equation
Coefficient of the equation
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Question # 8
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 # 9
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 # 10
If the roots of ax2 + 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 # 11
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 # 12
Choose an answer
0
1
2
3
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Question # 13
The roots of px2 - (p-q)x-q=0 are
Choose an answer
equal
Irrational
Rational
Imaginary
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Question # 14
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 # 15
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 # 16
Choose an answer
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Question # 17
The quadratic formula is
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Question # 18
w
-1
= ______
Choose an answer
0
1
w
w
2
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Question # 19
Roots of the equation x
2
- 7x + 10 = 0 are
Choose an answer
{2, 5}
{-2, 5}
{2,5}
{-2,-5}
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Question # 20
Choose an answer
0
1
2
None of these
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Question # 21
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 # 22
x
4
- 3x
3
+ 3x + 1 = 0 is called ______
Choose an answer
Reciprocal equation
Exponential equation
Radical equation
None of these
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Question # 23
Choose an answer
Only one real solution
Exactly three real solution
Exactly one rational solution
Non-real roots
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Question # 24
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 # 25
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 # 26
Which of the following is a factor of x
3
- 3x
2
+ 2x - 6
Choose an answer
x + 2
x + 3
x - 3
x - 4
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Question # 27
If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is
Choose an answer
0
2
1
5
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Question # 28
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 # 29
If a > 0, b > 0, c > 0, then the roots of the equation ax
2
+ 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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Question # 30
If the roots of ax
2
+ bx + c =0 are equal in magnitude but opposite in sign, then
Choose an answer
a = 0
b = 0
c = 0
None of these
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Question # 31
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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