Question # 1

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

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

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

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3

-3

2

0

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

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

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

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Vertex of parabola

Co-ordinates of parabola

Roots of the equation

Coefficient of the equation

x⁴- 3x³+ 3x + 1 = 0 is called ______

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Reciprocal equation

Exponential equation

Radical equation

None of these

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 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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1

2

0

4

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

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

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(x + 2)2(x - 1)

(x + 2)(x - 1)2

(x+2)(x2- x- 2)

(x + 2)2(x - 1)2

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

the largest degree of the terms in the polynomials is called

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terms of the polynomial

degree of a polynomial

co-efficient

monomial

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

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-1

0

2

1

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)

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

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1

2

1 and -7

-7

If b²- 4ac is positive then the roots of the equation are

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Real

Imaginary

Positive

Negative

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

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0

-1-w²

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

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Linear equation

Quadratic equation

Cubic equation

None of these

w^-1= ______

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0

1

w

w²

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0

1

2

3

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

The minimum value of the quadratic function f(x) = x2 +6x -2, is

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11

6

-11

13

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

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a+b=c+d

a+c=b+d

a+d=b+c

All are correct

Which of the following is factor of x11+a11, where n is an odd integer

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x-a

x+a

2x-a

2x+a

If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is

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1

3

2

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

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

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