Question # 1

The roots of (x - a)(x - b) = ab x2 are always

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Real

Depends upon a

Depends upon b

Depends upon a and b

The solution set of x²- 5x + 6 = 0 is

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{1, 3}

{2, 3}

{1, 2}

None of these

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Polynomial of degree 0

Polynomial of degree 1

Polynomial of degree 2

Polynomial of degree n

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 a polynomial p(x) is divided by x-c, then the remainder is

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p(x)

x-c

c

P(c)

w¹¹= ______

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0

1

w

w²

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

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α = β

αβ = 1

α = β

α = 1

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

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p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

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1

-1

5

2

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

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0

1

2

None of these

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

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

If ax + bx + c =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

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

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

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0

1

2

3

The sum of the roots of the equation x2 -6x +2 = 0 is

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-6

2

-2

6

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

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

w¹⁵= ______

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0

1

w

w²

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

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

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

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

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Real and equal

Real and distinct

Complex

None of these

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 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 b²- 4ac = 0 then the roots of the equation are

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Real and distinct

Real and equal

Imaginary

None of these

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

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

w⁴= ______

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0

1

w

w²

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

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

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