Question # 1

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Find a if 1 is a root of the equation x²+ ax + 2 = 0

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3

-3

2

0

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

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(0, 2π)

(-π, -0)

(0,π)

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

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

w^-1= ______

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0

1

w

w²

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)

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

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

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0

-1

1

2

w²⁹= ______

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0

1

w

w²

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

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

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

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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

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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 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)

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

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Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

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Root of the equation 3^x-1+ 3^1-x= is

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2

1

0

-1

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

w^-12= ______

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0

1

w

w²

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

(2 + w) (2 + w²) = ______

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1

2

3

0

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

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Real

Imaginary

Positive

Negative

(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 product of cube roots of unity is

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Zero

1

-1

None of these

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 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 maximum value of the quadratic function f(x) = 2x2-4x+7,is

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3

5

-3

-5

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ECAT Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers

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