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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
The maximum value of the quadratic function f(x) = 2x2-4x+7,is
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3
5
-3
-5
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Question # 2
If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is
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1
3
2
4
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Question # 3
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0
-1-w
2
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Question # 4
Each complex cube root of unity is square of
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itself
1
-1
the other
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Question # 5
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Two real roots
Two positive roots
Two negative roots
One positive and one negative root
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Question # 6
The quadratic equation 8 sec
2
θ
- 6 sec
θ
+1 = 0 has
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Infinitely many roots
Exactly two roots
Exactly four roots
No roots
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Question # 7
The roots of the equation ax
2
+ bx + c = 0 are complex/imaginary 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 # 8
(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if
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a+b=c+d
a+c=b+d
a+d=b+c
All are correct
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Question # 9
The polynomial x - a is a factor of the polynomial f(x) if and only if
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f(a) is positive
f(a) is negative
f(a) = 0
None of these
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Question # 10
If x
3
- x
2
+ 5x
+ 4 is divided by x - 2, then the reminder is
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0
2
18
14
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Question # 11
If the roots of ax2 + b =0 are real and distinct then
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ab > 0
a = 0
ab < 0
a > 0,b > 0
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Question # 12
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Question # 13
If a > 0, b > 0, c > 0, then the roots of the equation ax
2
+ bx + c = 0 are
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Real and negative
Non-real with negative real parts
Real and positive
Nothing can be said
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Question # 14
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 # 15
Sum of all the four forth roots of unity is
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1
-1
i
0
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Question # 16
The set of real roots of the equation log
(5x + 4)
(2x +3)
3
- log
(2x + 3)
(10x
2
+ 23x + 12) = 1 is
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{-1}
{-3/5}
Empty set
{-1/3}
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Question # 17
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Question # 18
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1
2
0
4
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Question # 19
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0
1
2
None of these
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Question # 20
If a parabola opens down, then its vertex is at the
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Right of the parabola
Left of parabola
Lowest point on the parabola
Highest point on the parabola
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Question # 21
The roots of the equation will be irrational if b
2
- 4ac is
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Positive and perfect square
Positive but not a perfect square
Negative
Zero
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Question # 22
In quadratic equation f(x) = ax
2
,if a >0, then the graph of parabola
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Opens up
Opens down
close up
symmetric w.r.t.x.axis
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Question # 23
A polynomial of arbitrary degree
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f(x) = o
f(x) = x
f(x) = a
f(x) = ax + b,a ≠ 0
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Question # 24
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Question # 25
(2 + w) (2 + w
2
) = ______
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1
2
3
0
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Question # 26
The synthetic division method is only used to divide a polynomial by
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quadratic equation
binomial
linear equation
monomial
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Question # 27
2x
3
+ 3x + 9 is a ______
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Polynomial of degree 3
Quadratic equation
Cubic equation
Polynomial of degree 2
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Question # 28
If sin
α
and cos
α
are the roots of the equation px
2
+ qx + r =0, then
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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 # 29
w
-12
= ______
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0
1
w
w
2
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Question # 30
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Polynomial of degree 0
Polynomial of degree 1
Polynomial of degree 2
Polynomial of degree n
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Question # 31
w
73
= ______
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0
1
w
w
2
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