Question # 1

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 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

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

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

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

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

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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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

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Linear equation

Quadratic equation

Cubic equation

None of these

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

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8

6

4

None of these

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

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p(x)

x-c

c

P(c)

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

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{-1}

{-3/5}

Empty set

{-1/3}

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

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Real and equal

Real and distinct

Complex

None of these

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

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c = 0

c = 0,b≠ 0

b = 0,c = 0

b = 0,c≠ 0

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

Root of the equation 3^x-1+ 3^1-x= is

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2

1

0

-1

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

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2, 8

1, 3

1, 8

2, 3

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

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Opens up

Opens down

close up

symmetric w.r.t.x.axis

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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

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5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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

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