Question # 1

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

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

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(x + 2)2(x - 1)

(x + 2)(x - 1)2

(x+2)(x2- x- 2)

(x + 2)2(x - 1)2

If the roots of 3x2+kx + 12 = 0 are equal then k = ______

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Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

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q = 0, r = 0,p ≠ 0

p = 0,qr≠ 0

r = 0,pq≠ 0

q = 0, pq≠ 0

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The solution of the quadratic equation x2 -7x + 10=0, is

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2

5

2,5

7

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

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

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Rational

Irrational

Complex

None of these

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Rational

Irrational

Non-real

Zero

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

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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0

-1-w²

The cube roots of 8 are

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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

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

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

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2, 8

1, 3

1, 8

2, 3

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

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

The quadratic formula is

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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

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

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(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

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

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Real and equal

Real and distinct

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

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

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

A quadratic equation has two

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roots

degree

variables

constants

w^-1= ______

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0

1

w

w²

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)

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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

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