Question # 1

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

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3

5

-3

-5

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

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

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x+1

2x+1

3x+1

2x-1

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c/a

-c/a

b/a

-b/a

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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)

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

w²⁸+ w³⁸= ______

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0

1

w

-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

w¹⁵= ______

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0

1

w

w²

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

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1

2

0

-1

w²⁹= ______

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0

1

w

w²

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0

1

2

None of these

The roots of the equation x2 +6x-7=0,are

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1

2

1 and -7

-7

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

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Rational

Irrational

Complex

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

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

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

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

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w^-12= ______

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0

1

w

w²

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,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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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

A quadratic equation has two

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roots

degree

variables

constants

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 value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

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2

1

-1

-2

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15

9

7

8

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

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0

1

2

3

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

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Reciprocal equation

Exponential equation

Radical equation

None of these

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

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

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