Question # 1

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b = c

a = c

b = 0

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

(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

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If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

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p²+ c/a

p²+ a/c

p²+ c/a

p²- c/a

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 x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

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1

0

4

None of these

If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

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0

±1

±5

±7

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

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-6

2

-2

6

If a polynomial P(x) is divided by x + a, then the remiander is

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P(a)

P(-a)

P(0)

None of these

The roots of px2 - (p-q)x-q=0 are

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equal

Irrational

Rational

Imaginary

The cube roots of 8 are

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If one root of the equation x²- 3x + a = 0 is 2 then a = ______

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0

1

2

3

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

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1

2

0

-4

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

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2, 8

1, 3

1, 8

2, 3

The minimum value of the quadratic function f(x) = 5 x 2-11,is

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7

-7

6

-11

There are ______ basic techniques for solving a quadratic equation

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Two

Three

Four

None of these

The root of the quadratic equation are

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3

2

1

4

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

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3

5

-3

-5

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

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

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0

2

18

14

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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 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

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

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

In quadratic equation y=ax³+bx+c, if b and c are both zero then the graph is

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Symmetric w.r.t.y-axis

Symmetric w.r.t.x-axis

Straight Line

Circle

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

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

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