Question # 1

If a polynomial P(x) is divided by x + a, then the remiander is

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P(a)

P(-a)

P(0)

None of these

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

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

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

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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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

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

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 f(x) = ax², and a>0, then the lowest point on the parabola is called.

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Vertex of parabola

Co-ordinates of parabola

Roots of the equation

Coefficient of the equation

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

w¹¹= ______

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0

1

w

w²

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 quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

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

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Rational

Irrational

Complex

None of these

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

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(5, 3, 1)

(4, 3, 2)

(5, 5, 1)

(6, 4, 1)

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

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The roots of ax2+bx+c=0 are

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Rational ⇔ b2 -4 ac ≥ 0

Irrational ⇔ b2-4 ac > 0

Real ⇔ b2-4 ac ≠ 0

Rational⇔ b2-4 ac = 0

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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If b²- 4ac is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

The roots of the equation ax²+ bx + c = 0 are real and equal if

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b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

The vertex of the graph of the quadratic function f(x) = x2 -10, is

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(0 , -10)

(-10,0)

(10,0)

(0,10)

The product of cube roots of unity is

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Zero

1

-1

None of these

If a parabola opens down, then its vertex is at the

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Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

Each complex cube root of unity is square of

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itself

1

-1

the other

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

w^-12= ______

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0

1

w

w²

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15

9

7

8

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