Question

If the polynomial $f(x)=ax^{3}+bx-c$ is divisible by the polynomial $g(x)=x^{2}+bx+c$, then ab=
(a) 1
(b) $\frac{1}{c}$
(c) -1
(d) $-\frac{1}{c}$

Answer 1

SOLUTION :  

The correct option is (a) : 1.

If f(x) is divisible by g(x), then remainder will be zero. So, to find the values, find the remainder and put it equal to zero to get the values .

Given : f(x) = ax³ + bx + c and g(x) = x² + bx + c  

DIVISION PROCESS IS IN THE ATTACHMENT .

We get remainder r(x) = bx - acx + ab²x + abc - c

bx - acx + ab²x + abc - c

= x( b - ac + ab²) + c ( ab - 1)  

since f(x) is exactly divisible by g(x) , therefore remainder should be zero.

So put   x( b - ac + ab²) + c ( ab - 1) = 0

c ( ab - 1) = 0

 ab - 1 = 0  , c≠0

ab = 1

Hence, the value of ab is 1 .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

Step-by-step explanation: