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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
Choose an answer
Polynomial of degree 0
Polynomial of degree 2
Quadratic equation
None of these
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Question # 2
The solution of the quadratic equation x2 -7x + 10=0, is
Choose an answer
2
5
2,5
7
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Question # 3
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 # 4
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 # 5
The graph of the quadratic equation is
Choose an answer
Straight line
Circle
Parabola
elipse
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Question # 6
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 # 7
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 # 8
There are ______ basic techniques for solving a quadratic equation
Choose an answer
Two
Three
Four
None of these
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Question # 9
If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is
Choose an answer
ay2 +2by+c=0
ay2+2by+4c=0
ay2+2by+c=0
ay2+by+4c=0
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Question # 10
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 # 11
In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is
Choose an answer
Straight line
Circle
Hyperbola
Symmetric w.r.t.0
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Question # 12
If a polynomial P(x) is divided by x - a, then the remainder is
Choose an answer
P(o)
P(-a)
P(a)
None of these
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Question # 13
Choose an answer
Two real roots
Two positive roots
Two negative roots
One positive and one negative root
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Question # 14
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 # 15
If x
3
+ ax
2
- a
2
x - a
3
is divided by x + a, then the remainder is
Choose an answer
0
a
3
2a
3
-2a
3
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Question # 16
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 # 17
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 # 18
Choose an answer
2
4
8
16
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Question # 19
Choose an answer
Only one real solution
Exactly three real solution
Exactly one rational solution
Non-real roots
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Question # 20
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 # 21
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 # 22
If
α
,
β
are the roots of ax
2
+ bx + c = 0 and
α
+ h,
β
+ h are the roots of px
2
+ qx + r=0, then h =
Choose an answer
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Question # 23
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 # 24
If x
2
+ px + 1 is a factor of ax
3
+ bx +c, then
Choose an answer
a
2
+ c
2
= -ab
a
2
- c
2
= -ab
a
2
- c
2
= ab
None of these
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Question # 25
Choose an answer
0
1
2
3
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Question # 26
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 # 27
Choose an answer
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Question # 28
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 # 29
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 # 30
(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 # 31
Choose an answer
0
1
2
None of these
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