Question # 1

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

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

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Rational

Irrational

Complex

None of these

The product of cube roots of unity is

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Zero

1

-1

None of these

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

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0

1

2

3

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

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p²+ c/a

p²+ a/c

p²+ c/a

p²- c/a

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

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2

1

0

-1

The solution of equation x2 + 2 = 0 in the set of real number is

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Infinite set

Singleton set

Null set

None of these

In quadratic equation y=ax³+bx+c, if b and c are both zero then the graph is

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Symmetric w.r.t.y-axis

Symmetric w.r.t.x-axis

Straight Line

Circle

If ax²+ bx + x = 0 is satisfied by every value of x, then

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b = 0, c = 0

c = 0

b = 0

a = b = c = 0

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

w¹⁵= ______

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0

1

w

w²

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b = c

a = c

b = 0

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

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ay2 +2by+c=0

ay2+2by+4c=0

ay2+2by+c=0

ay2+by+4c=0

x⁴- 3x³+ 3x + 1 = 0 is called ______

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Reciprocal equation

Exponential equation

Radical equation

None of these

A polynomial P(x)has a factor (x-a)if P(a) =

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a

x

1

0

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

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If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

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-i

2 + i

i

2 - i

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

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(-3,10)

(-3,-10)

(3,10)

(3,-10)

If x² + px + 1 is a factor of ax³+ bx +c, then

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a²+ c²= -ab

a²- c²= -ab

a²- c²= ab

None of these

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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

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

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

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

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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 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}

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1

-1

5

2

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

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c/a

-c/a

b/a

-b/a

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