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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
In quadratic equation y=ax
3
+bx+c, if b and c are both zero then the graph is
Choose an answer
Symmetric w.r.t.y-axis
Symmetric w.r.t.x-axis
Straight Line
Circle
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Question # 2
A quadratic equation in x is an equation that can be witten in the form
Choose an answer
ax
2
+ b = 0
ax
3
+b
2
+c=0
ax
2
+bx+c=0
ax
3
+bx
3
+cx=0
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Question # 3
If b
2
- 4ac = 0 then the roots of the equation are
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Real and distinct
Real and equal
Imaginary
None of these
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Question # 4
The graph of a quadratic function is
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Circle
Ellipse
Parabola
Hexagon
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Question # 5
If w is a cube root of unity then 1 + w + w
2
= ______
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1
2
0
-1
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Question # 6
If x - 1 is a factor of x4 - 5x2 + 4 then other factor is
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(x + 2)2(x - 1)
(x + 2)(x - 1)2
(x+2)(x2- x- 2)
(x + 2)2(x - 1)2
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Question # 7
The discriminant of the quadratic equation ax
2
+ bx + c = 0 is
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b
2
+ 4ac
b
2
- 4ac
4ac - b
2
a
2
- 4ac
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Question # 8
If the roots of x
2
+ ax + b = 0 are non-real, then for all real x, x
2
+ ax + b is
Choose an answer
Negative
Positive
Zero
Nothing can be said
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Question # 9
Choose an answer
b = c
a = c
a = c
b = 0
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Question # 10
The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in
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Question # 11
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
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6, 10
-6, -10
8, 8
-8, -8
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Question # 12
The solution of equation x2 + 2 = 0 in the set of real number is
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Infinite set
Singleton set
Null set
None of these
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Question # 13
5x
3
+ 3x - is a ______
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Polynomial of degree 3
Polynomial of degree 2
Polynomial of degree 1
Polynomial of degree 0
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Question # 14
The roots of the equation ax
2
+ bx + x = 0 are real and distinct if
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b
2
- 4ac <0
b
2
- 4ac = 0
b
2
- 4ac > 0
None of these
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Question # 15
If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is
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ay2 +2by+c=0
ay2+2by+4c=0
ay2+2by+c=0
ay2+by+4c=0
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Question # 16
(1+w)(1+w2)(1+w4)(1+w8)....50 factors
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0
-1
1
2
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Question # 17
The minimum value of the quadratic function f(x) = 5 x 2-11,is
Choose an answer
7
-7
6
-11
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Question # 18
A polynomial P(x)has a factor (x-a)if P(a) =
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a
x
1
0
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Question # 19
If b
2
- 4ac is positive then the roots of the equation are
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Real
Imaginary
Positive
Negative
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Question # 20
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 ______
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Addition
Subtraction
Multiplication
Division
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Question # 21
A quadratic equation has two
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roots
degree
variables
constants
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Question # 22
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 # 23
If the roots of ax
2
+ bx + c =0 are equal in magnitude but opposite in sign, then
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a = 0
b = 0
c = 0
None of these
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Question # 24
If the roots of 3x2+kx + 12 = 0 are equal then k = ______
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Question # 25
There are ______ basic techniques for solving a quadratic equation
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Two
Three
Four
None of these
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Question # 26
Choose an answer
n if n is even
0 for any natural number n
1 if in odd
None of these
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Question # 27
Another name of quadratic equation is
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Polynomial
2nd degree polynomial
Linear equation
simaltaneous equations
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Question # 28
The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is
Choose an answer
(-3,10)
(-3,-10)
(3,10)
(3,-10)
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Question # 29
The roots of the equation 2
2x
- 10.2
x
+ 16 = 0 are
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2, 8
1, 3
1, 8
2, 3
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Question # 30
Each complex cube root of unity is square of
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itself
1
-1
the other
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Question # 31
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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