# In Q. No. 14, c =A. bB. 2bC. 2b2D. – 2b

Given: f(x) = ax3 + bx – c is divisible by g(x) = x2 + bx + c

To find: The value of c.

Solution:

Since  f(x) = ax3 + bx – c is divisible by g(x) = x2 + bx + c

Now by division Method first we have to calculate the value of ab,

As f(x) is divisible by g(x), then remainder must be 0,

i.e.

(ab2 – ac + b)x + abc - c = 0

⇒ (ab2 – ac + b)x + c(ab – 1) = 0

(ab2 – ac + b)x = 0 and c(ab – 1) = 0

ab2 – ac + b = 0 ( x 0)

and ab
1 = 0 ( c 0)

ab – 1 = 0

ab = 1

Now take;

ab2 – ac + b = 0

(ab)b – ac + b = 0

Using ab = 1 we get;

b – ac + b = 0

2b – ac = 0

⇒ c = 2b/a ... (1)

Multiply and divide RHS of (1) by b

c = 2b/a = 2b2/ab

As ab = 1

So we get;

c = 2b2

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