Question # 1

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

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-5

5

0

1

The roots of the equations will be equal if b²- 4ac is

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Positive

Negative

1

Zero

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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Linear equation

Quadratic equation

Cubic equation

None of these

w²⁸+ w³⁸= ______

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0

1

w

-1

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If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

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a = 0

b = 0

c = 0

None of these

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

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quadratic equation

binomial

linear equation

monomial

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

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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(-1, 2)

(-1, 1)

(1, 2)

{-1}

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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1

2

0

4

the largest degree of the terms in the polynomials is called

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terms of the polynomial

degree of a polynomial

co-efficient

monomial

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 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

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

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 discriminant of the quadratic equation ax²+ bx + c = 0 is

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

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

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Real

Imaginary

Positive

Negative

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 ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

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

For the equation |x²| + |x| -6 =0, the roots are

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One and only one real number

Real with sum one

Real with sum zero

Real with product zero

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

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

The roots of px2 - (p-q)x-q=0 are

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equal

Irrational

Rational

Imaginary

If x² + px + 1 is a factor of ax³+ bx +c, then

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a²+ c²= -ab

a²- c²= -ab

a²- c²= ab

None of these

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