Question # 1

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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

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

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Addition

Subtraction

Multiplication

Division

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

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

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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

If the roots of ax²+ b = 0 are real and distinct then

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ab > 0

a = 0

ab < 0

a > 0, b > 0

The standard parabolic form of the equation f(x) = x² +4 x +1 is

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x(x+4)+1

(x+2)²-3

(x+4)³ + 9

x(x-2)²+1

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

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a

x

1

0

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)

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

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Vertex of parabola

Co-ordinates of parabola

Roots of the equation

Coefficient of the equation

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

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7

-2

6

1

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

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

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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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w¹¹= ______

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0

1

w

w²

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

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-7

7

0

None of these

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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 roots of ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

The root of the quadratic equation are

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3

2

1

4

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If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

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0

a³

2a³

-2a³

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

If the roots of ax2 + b =0 are real and distinct then

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ab > 0

a = 0

ab < 0

a > 0,b > 0

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

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

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8

6

4

None of these

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Rational

Irrational

Non-real

Zero

The minimum value of the quadratic function f(x) = 5 x 2-11,is

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7

-7

6

-11

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

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Real and equal

Real and distinct

Complex

None of these

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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers

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