Question # 1

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

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 graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

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

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

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p²+ c/a

p²+ a/c

p²+ c/a

p²- c/a

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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

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p(x)

x-c

c

P(c)

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

The condition for ax2 + bx c to be expressed as the product of linear polynomials is

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b4 - 4ac =0

b4- 4ac ≥0

b4- 4ac <0

b4= 4ac

If ax²+ bx + x = 0 is satisfied by every value of x, then

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b = 0, c = 0

c = 0

b = 0

a = b = c = 0

The roots of (b-c)x2+(c-a) x+a-b=0 are equal if

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2b = a+c

2a = b+c

2c = a+b

a + b + c =0

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

Which of the following is factor of x11+a11, where n is an odd integer

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x-a

x+a

2x-a

2x+a

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

The roots of the equation ax²+ bx + x = 0 are real and distinct if

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b²- 4ac <0

b²- 4ac = 0

b²- 4ac > 0

None of these

A polynomial P(x)has a factor (x-a)if P(a) =

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a

x

1

0

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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If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

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0

±1

±5

±7

In quadratic equation y=ax³+bx+c, if b and c are both zero then the graph is

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Symmetric w.r.t.y-axis

Symmetric w.r.t.x-axis

Straight Line

Circle

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

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b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

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

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

If w is a cube root of unity then 1 + w + w²= ______

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1

2

0

-1

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

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

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

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8

6

4

None of these

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

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1

2

0

-2

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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

(2 + w) (2 + w²) = ______

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1

2

3

0

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