Question # 1

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

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11

6

-11

13

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 quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

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

Find a if 1 is a root of the equation x²+ ax + 2 = 0

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3

-3

2

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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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

w²⁹= ______

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0

1

w

w²

w⁷³= ______

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0

1

w

w²

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

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-5

5

0

1

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

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1

0

4

None of these

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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

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

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

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4

6

8

10

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

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a

x

1

0

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

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0

a³

2a³

-2a³

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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

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x²+ Sx - P = 0

x²- Sx + P = 0

x²- Sx - P = 0

X²+ Sx + P = 0

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

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

If ax + bx + c =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

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

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(5, 3, 1)

(4, 3, 2)

(5, 5, 1)

(6, 4, 1)

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

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Real and equal

Real and distinct

Complex

None of these

If b²- 4ac = 0 then the roots of the equation are

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Real and distinct

Real and equal

Imaginary

None of these

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 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

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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