Question # 1

If a polynomial P(x) is divided by x + a, then the remiander is

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P(a)

P(-a)

P(0)

None of these

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

w²⁸+ w³⁸= ______

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0

1

w

-1

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1

2

0

4

If a polynomial P(x) is divided by x - a, then the remainder is

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P(o)

P(-a)

P(a)

None of these

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

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Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

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α = β

αβ = 1

α = β

α = 1

The minimum value of the quadratic function f(x) = x2 +6x -2, is

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11

6

-11

13

The standard parabolic form of the equation f(x) = x² +4 x +1 is

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x(x+4)+1

(x+2)²-3

(x+4)³ + 9

x(x-2)²+1

If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

The roots of (x - a)(x - b) = ab x2 are always

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Real

Depends upon a

Depends upon b

Depends upon a and b

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

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k=0

k=1

k=w

k=w2

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

Roots of the equation x²+ 2x + 3 = 0 are

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Real and equal

Real and distinct

Complex

None of these

The root of the quadratic equation are

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3

2

1

4

The vertex of the graph of the quadratic function f(x) = x2 -10, is

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(0 , -10)

(-10,0)

(10,0)

(0,10)

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

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p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

The roots of the equation x2 +6x-7=0,are

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1

2

1 and -7

-7

Roots of the equation x²+ 7x + 12 = 0 are

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

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0

1

2

3

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

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

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8

-16

-64

16

Roots of the equation x²+ 5x - 1 = 0 are

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Rational

Irrational

Complex

None of these

Roots of the equation 9x²- 12x + 4 = 0 are

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Real and equal

Real and distinct

Complex

None of these

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

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Addition

Subtraction

Multiplication

Division

Each complex cube root of unity is square of

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itself

1

-1

the other

The roots of the equation will be irrational if b²- 4ac is

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Positive and perfect square

Positive but not a perfect square

Negative

Zero

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

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Straight line

Circle

Hyperbola

Symmetric w.r.t.0

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers

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