Question # 1

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

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0

2

18

14

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

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

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k=0

k=1

k=w

k=w2

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

Each complex cube root of unity is square of

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itself

1

-1

the other

Which of the following is a factor of x³- 3x²+ 2x - 6

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x + 2

x + 3

x - 3

x - 4

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 largest degree of the terms in the polynomials is called

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terms of the polynomial

degree of a polynomial

co-efficient

monomial

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

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

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

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

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15

9

7

8

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-1

0

2

1

Sum of all the four forth roots of unity is

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1

-1

i

0

The maximum value of the quadratic function f(x) = -2x2+20x,is

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4

3

50

7

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0

-1-w²

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

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

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Positive

Negative

1

Zero

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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

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

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

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2

1

-1

-2

Find a if 1 is a root of the equation x²+ ax + 2 = 0

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3

-3

2

0

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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

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 quadratic formula is

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w²⁹= ______

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0

1

w

w²

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

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