Question # 1

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

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Negative

Positive

Zero

Nothing can be said

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

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Positive

Negative

1

Zero

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

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

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Real and equal

Real and distinct

Complex

None of these

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1

-1

5

2

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 root of the quadratic equation are

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3

2

1

4

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Reciprocal equation

Exponential equation

Radical equation

None of these

The standard form of the quadratic function f(x) = -x² +4x+2, is

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(x-2)²+6

-(x-2)² + 6

(x-3)²+5

(x+4)²-7

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)

The synthetic division method is only used to divide a polynomial by

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quadratic equation

binomial

linear equation

monomial

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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

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

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1

2

0

-4

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

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

If x² + px + 1 is a factor of ax³+ bx +c, then

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a²+ c²= -ab

a²- c²= -ab

a²- c²= ab

None of these

x⁴- 3x³+ 3x + 1 = 0 is called ______

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Reciprocal equation

Exponential equation

Radical equation

None of these

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

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(5, 3, 1)

(4, 3, 2)

(5, 5, 1)

(6, 4, 1)

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

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

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0

a³

2a³

-2a³

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4

6

8

10

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

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

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3

5

-3

-5

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 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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n if n is even

0 for any natural number n

1 if in odd

None of these

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

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

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

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Opens up

Opens down

close up

symmetric w.r.t.x.axis

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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

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