Question # 1

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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

The cube roots of 8 are

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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c/a

-c/a

b/a

-b/a

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

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8

6

4

None of these

The discriminant of the quadratic equation ax²+ bx + c = 0 is

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b²+ 4ac

b²- 4ac

4ac - b²

a²- 4ac

Roots of the equation x²- 7x + 10 = 0 are

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

w^-12= ______

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0

1

w

w²

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

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 maximum value of the quadratic function f(x) = -2x2+20x,is

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4

3

50

7

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

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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

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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

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

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

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

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-6

2

-2

6

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

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 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

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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

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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n if n is even

0 for any natural number n

1 if in odd

None of these

If a polynomial P(x) is divided by x - a, then the remainder is

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P(o)

P(-a)

P(a)

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

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

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Rational

Irrational

Non-real

Zero

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

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