Question # 1

The synthetic division method is only used to divide a polynomial by

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quadratic equation

binomial

linear equation

monomial

Which of the following is a factor of x³- 3x²+ 2x - 6

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x + 2

x + 3

x - 3

x - 4

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

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

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-6

2

-2

6

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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

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

The maximum value of the quadratic function f(x) = -2x2+20x,is

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4

3

50

7

The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

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4

64

8

All values of k

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

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w⁷³= ______

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0

1

w

w²

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)

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0

-1-w²

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 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

If 2x^1/3+ 2x^-1/3= 5, then x is equal to

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1 or -1

2 or 1/2

8 or 1/8

4 or 1/4

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

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Real

Imaginary

Positive

Negative

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

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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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

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

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x+1

2x+1

3x+1

2x-1

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 one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is

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0

2

1

5

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4

6

8

10

For any integer k, wⁿ= ______ when n = 3k

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1

2

0

-4

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

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Real and equal

Real and distinct

Complex

None of these

(2 + w) (2 + w²) = ______

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1

2

3

0

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15

9

7

8

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 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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