Question

If ax3 + bx2+ cx + d is exactly divisible by (x + 1) and (x + 2), then which of the following is true(A) 3a – 3b + d = 0(B) 8a – b + 2d = 0 (C) 5a – 2b + 3d = 0(D) 6a – 2b + d = 0

Answer 1

Answer:

D

Step-by-step explanation:

Let f(x) = ax³ + bx²+ cx + d

Since f(x) is exactly divisible by (x + 1) and (x + 2),

f(-1) = 0,

f(-2) = 0 by Factor's theorem.

f(-1) = -a + b - c + d = 0-----(1)

f(-2) = -8a + 4b -2c + d = 0----(2)

By eliminating c from (1) and (2) we get

(D) 6a - 2b + d = 0.....Answer

Answer 2

Answer:

(D) 6a - 2b + d = 0

Step-by-step explanation:

Given polynomial is:

f(x) = ax³ + bx² + cx + d

f(x) is exactly divisible by (x + 1) and (x + 2) then,

By factor's theorem,

f(-1) = 0 and f(-2) = 0

f(-1) = a(-1)³ + b(-1)² + c(-1) + d = 0

        -a + b - c + d = 0    ..........(i)

f(-2) = a(-2)³ + b(-2)² + c(-2) + d = 0

         -8a + 4b -2c + d - 0   ..........(ii)

Now, eliminating c from equation (i) and (ii) we get,

6a - 2b + d = 0