Question # 1

The roots of the equation ax²+ bx + x = 0 are real and distinct if

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b²- 4ac <0

b²- 4ac = 0

b²- 4ac > 0

None of these

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-1

0

2

1

If a parabola opens down, then its vertex is at the

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Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

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

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-6

2

-2

6

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

Roots of the equation x²- x = 2 are

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{2, -1}

{1, 0}

{2, 1}

{-2, 1}

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)

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

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quadratic equation

binomial

linear equation

monomial

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 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

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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For the equation |x²| + |x| -6 =0, the roots are

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One and only one real number

Real with sum one

Real with sum zero

Real with product zero

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

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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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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

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

4^1+x+ 4^1-x= 10 is called

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Reciprocal equation

Exponential equation

Radical equation

None of these

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

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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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0

1

2

3

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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c/a

-c/a

b/a

-b/a

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0

1

2

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

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

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

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

w²⁸+ w³⁸= ______

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0

1

w

-1

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