Question # 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)

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0

-1-w²

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

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

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p(x)

x-c

c

P(c)

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 positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

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4

64

8

All values of k

w¹⁵= ______

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0

1

w

w²

Roots of the equation 9x²- 12x + 4 = 0 are

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Real and equal

Real and distinct

Complex

None of these

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

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0

7

-7

5

Another name of quadratic equation is

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Polynomial

2nd degree polynomial

Linear equation

simaltaneous equations

w²⁹= ______

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0

1

w

w²

The root of the quadratic equation are

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3

2

1

4

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(-1, 2)

(-1, 1)

(1, 2)

{-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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If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

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a = 0

b = 0

c = 0

None of these

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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

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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1

2

0

4

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

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

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-6

2

-2

6

Each complex cube root of unity is square of

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itself

1

-1

the other

Roots of the equation 2x²- 7x + 3 = 0 are

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Rational

Irrational

Complex

None of these

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

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

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2

4

8

16

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

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

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

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quadratic equation

binomial

linear equation

monomial

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