Question # 1

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

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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

w⁷³= ______

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0

1

w

w²

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 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 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 graph of the quadratic equation is

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Straight line

Circle

Parabola

elipse

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1

-1

5

2

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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If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

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

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0

-1

1

2

In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are

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6, 10

-6, -10

8, 8

-8, -8

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

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(-3,10)

(-3,-10)

(3,10)

(3,-10)

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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 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

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

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

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Real and equal

Real and distinct

Complex

None of these

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

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

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x²+ Sx - P = 0

x²- Sx + P = 0

x²- Sx - P = 0

X²+ Sx + P = 0

If a polynomial P(x) is divided by x - a, then the remainder is

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P(o)

P(-a)

P(a)

None of these

The roots of the equation ax²+ bx + c = 0 are real and equal if

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b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

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

The roots of px2 - (p-q)x-q=0 are

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equal

Irrational

Rational

Imaginary

The roots of the equation will be irrational if b²- 4ac is

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Positive and perfect square

Positive but not a perfect square

Negative

Zero

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

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Rational

Irrational

Complex

None of these

If b²- 4ac is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers

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