Question # 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

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

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1

0

4

None of these

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The discriminant of the quadratic equation ax²+ bx + c = 0 is

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

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8

-16

-64

16

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

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

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

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7

-2

6

1

w¹⁵= ______

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0

1

w

w²

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 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

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

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-5

5

0

1

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

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-6

2

-2

6

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

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

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a = 0

b = 0

c = 0

None of these

The minimum value of the quadratic function f(x) = x2 +6x -2, is

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11

6

-11

13

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

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c = 0

c = 0,b≠ 0

b = 0,c = 0

b = 0,c≠ 0

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5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

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

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0

2

18

14

The product of the four fourth roots of unity is

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0

1

-1

None of these

The roots of (b-c)x2+(c-a) x+a-b=0 are equal if

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2b = a+c

2a = b+c

2c = a+b

a + b + c =0

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

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Rational

Irrational

Complex

None of these

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 equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is

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1

3

2

4

2x³+ 3x + 9 is a ______

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Polynomial of degree 3

Quadratic equation

Cubic equation

Polynomial of degree 2

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

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

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