Question # 1

The product of the four fourth roots of unity is

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0

1

-1

None of these

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

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3

5

-3

-5

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

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

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0

7

-7

5

The sum of the roots of the equation x2 -6x +2 = 0 is

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-6

2

-2

6

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

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

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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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

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

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(0, 2π)

(-π, -0)

(0,π)

None of these

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2

4

8

16

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

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11

6

-11

13

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

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7

-2

6

1

Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

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q = 0, r = 0,p ≠ 0

p = 0,qr≠ 0

r = 0,pq≠ 0

q = 0, pq≠ 0

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

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Opens up

Opens down

close up

symmetric w.r.t.x.axis

Roots of the equation x²- 7x + 10 = 0 are

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

x⁴- 3x³+ 3x + 1 = 0 is called ______

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Reciprocal equation

Exponential equation

Radical equation

None of these

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

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

The solution of equation x2 + 2 = 0 in the set of real number is

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Infinite set

Singleton set

Null set

None of these

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

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0

2

18

14

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

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0

a³

2a³

-2a³

If b²- 4ac is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

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

The solution of the quadratic equation x2 -7x + 10=0, is

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2

5

2,5

7

The solution set of x²- 5x + 6 = 0 is

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{1, 3}

{2, 3}

{1, 2}

None of these

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(-1, 2)

(-1, 1)

(1, 2)

{-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

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n if n is even

0 for any natural number n

1 if in odd

None of these

The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is

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a > 0

a < 0

a≠ 0

a≠ 0,b ≠ 0

The roots of ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

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