Question # 1

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

If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is

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0

2

1

5

w²⁸+ w³⁸= ______

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0

1

w

-1

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

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a

x

1

0

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

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

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Rational

Irrational

Complex

None of these

w¹⁵= ______

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0

1

w

w²

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

Another name of quadratic equation is

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Polynomial

2nd degree polynomial

Linear equation

simaltaneous equations

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

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0

1

2

3

The roots of the equation ax²+ bx + x = 0 are real and distinct if

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b²- 4ac <0

b²- 4ac = 0

b²- 4ac > 0

None of these

The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

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b = c

a = c

b = 0

A quadratic equation has two

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roots

degree

variables

constants

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

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

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Positive

Negative

Real

None of these

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

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Positive

Negative

1

Zero

If ax + bx + c =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

Roots of the equation 9x²- 12x + 4 = 0 are

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Real and equal

Real and distinct

Complex

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

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 b²- 4ac = 0 then the roots of the equation are

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Real and distinct

Real and equal

Imaginary

None of these

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The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

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If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

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x²+ Sx - P = 0

x²- Sx + P = 0

x²- Sx - P = 0

X²+ Sx + P = 0

w⁷³= ______

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0

1

w

w²

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

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

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

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Rational

Irrational

Complex

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

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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers

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