Question

In Q. No. 14, c =
A. b
B. 2b
C. 2b²
D. – 2b

Answer 1

${2b}^{2}$

Answer 2

C. 2b²

Step-by-step explanation:

The question is missing. If f(x) = ax³ + bx - c is divisible by g(x) = x² + bx + c, find C.

Let us divide f(x) by g(x):

ax³ + bx - c / x² + bx + c = ax -ab and remainder bx-acx +ab²x +abc -c

The remainder must be zero.

So bx-acx +ab²x +abc -c = 0 for all x.

x (b -ac+ ab²) + c (ab-1) = 0 ---(1)

c(ab-1) = 0

Since C is not zero, ab-1 = 0, ab = 1

So we have x = 1 and ab = 1.

Substituting in (1), we get:

b - ac + ab² = 0

b + ab² - ac = 0

b (a + ab) - ac = 0

Substituting a = 1/b and ab = 1, we get:

b (1+1) - 1/b *c = 0

2b - 1/b*c = -2b

c = -1/b *-2b

c = 2b = b/1  

c = 2b²

Option C is the answer.