Question # 1

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0

-1-w²

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

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-5

5

0

1

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

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3

-3

2

0

w²⁸+ w³⁸= ______

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0

1

w

-1

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

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P(o)

P(-a)

P(a)

None of these

The cube roots of 8 are

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(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

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a+b=c+d

a+c=b+d

a+d=b+c

All are correct

The solution set of x²- 5x + 6 = 0 is

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{1, 3}

{2, 3}

{1, 2}

None of these

Roots of the equation 2x²- 7x + 3 = 0 are

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Rational

Irrational

Complex

None of these

(2 + w) (2 + w²) = ______

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1

2

3

0

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

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-7

7

0

None of these

w⁷³= ______

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0

1

w

w²

The graph of the quadratic equation is

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Straight line

Circle

Parabola

elipse

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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 value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

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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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Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

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Positive

Negative

Real

None of these

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

w^-12= ______

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0

1

w

w²

Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always

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Positive

Negative

Real

None of these

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n if n is even

0 for any natural number n

1 if in odd

None of these

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

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

A quadratic equation in x is an equation that can be witten in the form

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ax²+ b = 0

ax³ +b²+c=0

ax² +bx+c=0

ax³ +bx³+cx=0

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 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

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

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2

1

-1

-2

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

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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

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

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