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MBA Factors CH 15 LD 2.3

Total questions: 25

Worksheet time: 50mins

Name
Class
Date
1.

If α, β are the roots of the quadratic equation x2 + mx + 1 = 0 and γ, δ\delta  are the roots of the equation x2 + nx + 1 = 0, then the value of (α − γ) (β − γ) (α + δ\delta   )(β + δ\delta  ) is equal to

a)

n2 − m2.

b)

m2 − n2 .

c)

2 m2 − n2 .

d)
None of the above
2.

Find the roots of the quadratic equation bx2 − 2ax + a = 0

a)

bb±ab\frac{\sqrt[]{b}}{\sqrt[]{b\pm\sqrt[]{a-b}}}  

b)

ab±ab\frac{\sqrt[]{a}}{\sqrt[]{b\pm\sqrt[]{a-b}}}  

c)

aa±ab\frac{\sqrt[]{a}}{\sqrt[]{a}\pm\sqrt[]{a-b}}  

d)

aa± a+b\frac{\sqrt[]{a}}{\sqrt[]{a}\pm\ \sqrt[]{a+b}}  

3.

If x2 + 3x − 10 is a factor of 3x4 + 2x3 − ax2 + bx − a + b − 4, then the closest approximate values of a and b are

a)
25, 43
b)
52, 43
c)
52, 67
d)
None of the above
4.

If x is real, the smallest value of the expression 3x2 − 4x + 7 is:

a)

2/3

b)
¾
c)

7/9

d)
None of the above
5.
If 0 < p < 1 then the roots of the equation (1 − p) x 2 + 4x + p = 0 are ___?
a)
Real and of opposite sign.
b)
Real and both negative
c)
Imaginary
d)
Real and both positive
6.

The number of possible real solution(s) of y in the equation y2 − 2y cos x + 1 = 0 is____?

a)
0
b)
1
c)
2
d)
3
7.

A polynomial ax3 + bx2 + cx + d intersects the x−axis at 1 and −1, and y-axis at 2. The value of b is:

a)
− 2
b)
0
c)
1
d)
2
8.

If x3 − mx2 + nx − p = 0 has three roots α, β, γ. If we add 3 in each of the roots of x3 − mx2 + nx − p = 0 then we get the roots of the equation x3 − ax2 + bx − 27 = 0. What is the value of p + 9m + 3n.

a)
0
b)
1
c)
−54
d)
54
9.

If the roots of the equation x3 + qx2 + rx + s = 0 are in GP, then which of the following is true:

a)

r 2 = q2 s

b)

r 3 = q3 s

c)

r = qs2

d)

r = qs3

10.

The graph of ax2 + bx + c is shown below. Then which of the following is true?

a)
a < 0, b < 0, c > 0
b)
a < 0, b < 0, c < 0
c)
a < 0, b > 0, c > 0
d)
a < 0, b > 0, c < 0
11.

If ‘x’ is a real number then what is the number of solutions for the equation: (x8 + 12)1/2 = x4 − 2

a)
0
b)
1
c)
2
d)
Cannot be determined
12.

How many integer values of ‘p’ are there such that the inequality x2 + 4px + (p + 3) > 0 is true for all values of x?

(a)  

13.

If g (x)=x3px2qx2rg\ \left(x\right)=x^3-px^2-\frac{qx}{2}-r  can be factorized as (x − p) (x − q) (x − r), then f(4) = ?

(a)  

14.

The roots of x3 − px2 + qx − r = 0 are a, b, c while the roots of x3 + wx2 + yz − 47 = 0 are a + 2, b + 2, c + 2, Then the value of 4p + 2q + r=?

(a)  

15.

One of the roots of the equation x2 + bx + 3b = 0 (b ∈ R) is thrice the other root, What is the value of 3b.

(a)  

16.

One of the roots of the equation x2 + bx + 3b = 0 (b ∈ R) is thrice the other root, Which of the following options correctly represents roots of the equation x2 − 33x + 17b = 0

a)
b, b + 1
b)
b − 1, b
c)
b − 1, b + 1
d)
None of these
17.

The roots of x2 + 5x + a = 0 are p and q while the roots of x2 + 23x + b = 0 are q and r. If p, q, r are in an Arithmetic Progression then the value of |a × b| = ?

(a)  

18.

f (x) = (x − 2)(x2 + 2x + 5)

If a, b, c are the roots of f(x) = 0, then the value of a3 + b3 + c3 would be equal to?

(a)  

19.

If f(x) = px2 + qx + r and f(x) is exactly divisible by (x + 2) and (x + 3) but leaves remainder of 7 when divided by (x − 1), find the approximate value of q?

(a)  

20.

If f (x)=4x7 xf\ \left(x\right)=4x-7\ \sqrt[]{x}   , which of the following statements is true about the roots of the equation f(x) = 2.

a)
It has only one real root which is not an integer.
b)
It has no real root
c)
It has one real root which is a positive integer.
d)
It has two real roots.
21.

If the equation ax2 + bx + a = 0(a > 0) has real and positive roots then which of the following is always true?

a)
b < 2a
b)
b < 0
c)
b ≤ −2a
d)
All the options are true
22.
If p, q, r are real and (x − p)(x − q)+(x − q)(x − r)+(x − r)(x − p)=0 if p ≠ q ≠ r then which of the following options is true?
a)
Roots of the given equations are imaginary.
b)
Roots of the given equation are real.
c)
Roots of the given equation are equal.
d)
None of these
23.

If f(x) = px2 + qx + r and g(x) = rx2 + qx + p. If one root of f(x) = 0 is 2 and one root of g(x) = 0 is ¼, then find the sum of the roots of f(x) and g(x).

(a)  

24.

The number of distinct points at which the curve y3 − 4y2 + x2 − 5x + 3y = 0 intersects either the y-axis or the x-axis is.

(a)  

25.

If the sum of the roots of the quadratic equation px2 + qx + r = 0 is equal to the sum of the square of their reciprocals, mark all the correct statements.

a)
r/p, p/q and q/r are in A. P.
b)
p/ r, q/p and r/q are in G. P.
c)
p/r, q/p and r/q are in H. P.
d)
Option (a) and (c) both.