Question # 1

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)

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 roots of the equation 4x - 3.2x+2 + 32 = 0 would include

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1 and 3

1 and 4

1 and 2

2 and 3

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}

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

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-7

7

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

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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 x³+ ax²- a²x - a³is divided by x + a, then the remainder is

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0

a³

2a³

-2a³

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

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1

2

0

-1

4^1+x+ 4^1-x= 10 is called

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Reciprocal equation

Exponential equation

Radical equation

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

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n if n is even

0 for any natural number n

1 if in odd

None of these

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

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1

0

4

None of these

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

Which of the following is a factor of x³- 3x²+ 2x - 6

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x + 2

x + 3

x - 3

x - 4

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

Sum of all the four forth roots of unity is

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1

-1

i

0

2x³+ 3x + 9 is a ______

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Polynomial of degree 3

Quadratic equation

Cubic equation

Polynomial of degree 2

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

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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c/a

-c/a

b/a

-b/a

Roots of the equation x²+ 5x - 1 = 0 are

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Rational

Irrational

Complex

None of these

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

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

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2

1

0

-1

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The roots of the equation will be irrational if b²- 4ac is

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Positive and perfect square

Positive but not a perfect square

Negative

Zero

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