Question # 1

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

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

The roots of ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

(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

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

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1

0

4

None of these

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

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

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1

2

0

-1

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

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 the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is

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1

3

2

4

w⁴= ______

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0

1

w

w²

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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

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P(o)

P(-a)

P(a)

None of these

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

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Positive

Negative

1

Zero

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)

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

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8

6

4

None of these

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

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Rational

Irrational

Complex

None of these

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

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0

7

-7

5

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Rational

Irrational

Non-real

Zero

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

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Straight line

Circle

Hyperbola

Symmetric w.r.t.0

The polynomial x - a is a factor of the polynomial f(x) if and only if

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f(a) is positive

f(a) is negative

f(a) = 0

None of these

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}

Sum of all the four forth roots of unity is

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1

-1

i

0

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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

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

Another name of quadratic equation is

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Polynomial

2nd degree polynomial

Linear equation

simaltaneous equations

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

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

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