Question # 1

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

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1 and 3

1 and 4

1 and 2

2 and 3

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

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

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

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The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

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0

2

18

14

w²⁸+ w³⁸= ______

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0

1

w

-1

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0

1

2

3

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Linear equation

Quadratic equation

Cubic equation

None of these

(2 + w) (2 + w²) = ______

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1

2

3

0

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Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

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c = 0

c = 0,b≠ 0

b = 0,c = 0

b = 0,c≠ 0

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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

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quadratic equation

binomial

linear equation

monomial

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 expression x2 - x + 1 has

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One proper linear factor

No proper linear factor

Two proper linear factors

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

The standard parabolic form of the equation f(x) = x² +4 x +1 is

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x(x+4)+1

(x+2)²-3

(x+4)³ + 9

x(x-2)²+1

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

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4

6

8

10

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1

2

0

4

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

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2

1

-1

-2

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

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8

-16

-64

16

The roots of the equation ax²+ bx + c = 0 are real and equal if

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b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

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)

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 quadratic formula is

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If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

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8

6

4

None of these

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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test MCQs With Answers

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