Question # 1

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

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

If w is a cube root of unity then 1 + w + w²= ______

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1

2

0

-1

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

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1

2

1 and -7

-7

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15

9

7

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 (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

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0

-1-w²

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

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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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

w¹¹= ______

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0

1

w

w²

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

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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

Sum of all the four forth roots of unity is

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1

-1

i

0

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

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 a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

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0

±1

±5

±7

If a > 0, b > 0, c > 0, then the roots of the equation ax²+ bx + c = 0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

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2

4

8

16

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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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w⁷³= ______

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0

1

w

w²

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Linear equation

Quadratic equation

Cubic equation

None of these

The roots of the equations will be equal if b²- 4ac is

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Positive

Negative

1

Zero

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0

1

2

3

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

The graph of the quadratic equation is

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Straight line

Circle

Parabola

elipse

If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

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