Question # 1

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

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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

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 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

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

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Linear equation

Quadratic equation

Cubic equation

None of these

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-1

0

2

1

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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

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quadratic equation

binomial

linear equation

monomial

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

If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

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-i

2 + i

i

2 - i

w²⁸+ w³⁸= ______

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0

1

w

-1

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 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

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

w^-1= ______

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0

1

w

w²

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 the equations will be equal if b²- 4ac is

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Positive

Negative

1

Zero

w⁴= ______

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0

1

w

w²

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

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

The product of cube roots of unity is

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Zero

1

-1

None of these

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

The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is

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a > 0

a < 0

a≠ 0

a≠ 0,b ≠ 0

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

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1

2

0

-2

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

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p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

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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