Question # 1

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is

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8

12

10

14

(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

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

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 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

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

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Positive

Negative

1

Zero

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0

1

2

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

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

The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

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4

64

8

All values of k

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

The minimum value of the quadratic function f(x) = x2 +6x -2, is

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11

6

-11

13

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

Each complex cube root of unity is square of

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itself

1

-1

the other

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

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b = c

a = c

b = 0

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

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

If w is a cube root of unity then 1 + w + w²= ______

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1

2

0

-1

For any integer k, wⁿ= ______ when n = 3k

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1

2

0

-4

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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

Roots of the equation x²+ 7x + 12 = 0 are

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

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