Question # 1

For the equation |x²| + |x| -6 =0, the roots are

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One and only one real number

Real with sum one

Real with sum zero

Real with product zero

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

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1

2

1 and -7

-7

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Rational

Irrational

Non-real

Zero

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A quadratic equation in x is an equation that can be witten in the form

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ax²+ b = 0

ax³ +b²+c=0

ax² +bx+c=0

ax³ +bx³+cx=0

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

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Rational

Irrational

Complex

None of these

If 2x^1/3+ 2x^-1/3= 5, then x is equal to

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1 or -1

2 or 1/2

8 or 1/8

4 or 1/4

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

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Rational

Irrational

Complex

None of these

Each complex cube root of unity is square of

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itself

1

-1

the other

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

A quadratic equation has two

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roots

degree

variables

constants

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

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Opens up

Opens down

close up

symmetric w.r.t.x.axis

If a parabola opens down, then its vertex is at the

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Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

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

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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

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Straight line

Circle

Hyperbola

Symmetric w.r.t.0

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

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x + 2

x + 3

x - 3

x - 4

w¹¹= ______

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0

1

w

w²

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

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a+b=c+d

a+c=b+d

a+d=b+c

All are correct

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)

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

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

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

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0

a³

2a³

-2a³

The product of cube roots of unity is

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Zero

1

-1

None of these

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

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{-1}

{-3/5}

Empty set

{-1/3}

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

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

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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

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

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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers

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