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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
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 # 2
If x
3
+ 4x
3
- 2x +5 is divided by x - 1, then the reminder is
Choose an answer
8
6
4
None of these
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Question # 3
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 # 4
The maximum value of the quadratic function f(x) = 2x2-4x+7,is
Choose an answer
3
5
-3
-5
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Question # 5
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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Question # 6
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 # 7
The discriminant of the quadratic equation ax
2
+ bx + c = 0 is
Choose an answer
b
2
+ 4ac
b
2
- 4ac
4ac - b
2
a
2
- 4ac
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Question # 8
Choose an answer
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Question # 9
The maximum value of the quadratic function f(x) = -2x2+20x,is
Choose an answer
4
3
50
7
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Question # 10
If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is
Choose an answer
0
±1
±5
±7
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Question # 11
Choose an answer
Linear equation
Quadratic equation
Cubic equation
None of these
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Question # 12
Choose an answer
b = c
a = c
a = c
b = 0
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Question # 13
Each complex cube root of unity is square of
Choose an answer
itself
1
-1
the other
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Question # 14
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 # 15
Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when
Choose an answer
q = 0, r = 0,p ≠ 0
p = 0,qr≠ 0
r = 0,pq≠ 0
q = 0, pq≠ 0
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Question # 16
If x
2
- 7x + a has remainder 1 when divided by x + 1, then a = ______
Choose an answer
-7
7
0
None of these
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Question # 17
Choose an answer
0
1
2
3
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Question # 18
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Question # 19
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Question # 20
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 # 21
Roots of the equation x
2
+ 5x - 1 = 0 are
Choose an answer
Rational
Irrational
Complex
None of these
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Question # 22
The graph of a quadratic function is
Choose an answer
Circle
Ellipse
Parabola
Hexagon
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Question # 23
Which of the following is factor of x11+a11, where n is an odd integer
Choose an answer
x-a
x+a
2x-a
2x+a
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Question # 24
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 # 25
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 # 26
The minimum value of the quadratic function f(x) = x2 +6x -2, is
Choose an answer
11
6
-11
13
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Question # 27
Choose an answer
c/a
-c/a
b/a
-b/a
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Question # 28
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 # 29
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 # 30
The polynomial x - a is a factor of the polynomial f(x) if and only if
Choose an answer
f(a) is positive
f(a) is negative
f(a) = 0
None of these
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Question # 31
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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