Question # 1

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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

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a > 0

a < 0

a≠ 0

a≠ 0,b ≠ 0

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

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1

0

4

None of these

The minimum value of the quadratic function f(x) = 5 x 2-11,is

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7

-7

6

-11

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0

1

2

3

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

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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

Roots of the equation x²+ 7x + 12 = 0 are

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

The maximum value of the quadratic function f(x) = -2x2+20x,is

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4

3

50

7

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

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

For any integer k, wⁿ= ______ when n = 3k

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1

2

0

-4

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4

6

8

10

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 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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The solution set of x²- 5x + 6 = 0 is

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{1, 3}

{2, 3}

{1, 2}

None of these

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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Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

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q = 0, r = 0,p ≠ 0

p = 0,qr≠ 0

r = 0,pq≠ 0

q = 0, pq≠ 0

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

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3

-3

2

0

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

Which of the following is a factor of x³- 3x²+ 2x - 6

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x + 2

x + 3

x - 3

x - 4

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

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If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

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1

2

0

-2

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)

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

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