Question # 1

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

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

w^-12= ______

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0

1

w

w²

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

(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 standard form of the quadratic function f(x) = -x² +4x+2, is

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(x-2)²+6

-(x-2)² + 6

(x-3)²+5

(x+4)²-7

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

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Negative

Positive

Zero

Nothing can be said

The quadratic formula is

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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 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

The expression x2 - x + 1 has

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One proper linear factor

No proper linear factor

Two proper linear factors

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

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

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c/a

-c/a

b/a

-b/a

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

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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

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4

3

50

7

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

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Real and equal

Real and distinct

Complex

None of these

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1

-1

5

2

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

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2

1

-1

-2

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b = c

a = c

b = 0

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

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

w¹⁵= ______

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0

1

w

w²

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 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

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

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 is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

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