Question # 1

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

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7

-2

6

1

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 the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

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

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x + 2

x + 3

x - 3

x - 4

2x³+ 3x + 9 is a ______

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Polynomial of degree 3

Quadratic equation

Cubic equation

Polynomial of degree 2

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0

1

2

None of these

A quadratic equation has two

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roots

degree

variables

constants

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1

2

0

4

If 2x^1/3+ 2x^-1/3= 5, then x is equal to

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1 or -1

2 or 1/2

8 or 1/8

4 or 1/4

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 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

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

w^-1= ______

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0

1

w

w²

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

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ay2 +2by+c=0

ay2+2by+4c=0

ay2+2by+c=0

ay2+by+4c=0

w⁴= ______

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0

1

w

w²

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

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Positive

Negative

1

Zero

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

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The graph of the quadratic equation is

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Straight line

Circle

Parabola

elipse

(2 + w) (2 + w²) = ______

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1

2

3

0

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15

9

7

8

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

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

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1

2

1 and -7

-7

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

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

The roots of ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

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4

6

8

10

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

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 x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

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-5

5

0

1

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

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