Question

find the value of a if x³-ax²+bx-a is exactly divisible by (x+2)​

Answer 1

-2 is a root of p(x) = x³ - ax² + bx - a = 0 if (x + 2) is a factor.

$p(-2)=(-2)^3-a(-2)^2+b(-2)-a=0 \\ \\ p(-2)=-8-a(4)-2b-a=0 \\ \\ p(-2)=-8-4a-2b-a=0 \\ \\ p(-2)=-8-2b-5a=0 \\ \\ \\ \Rightarrow\ -8-2b-5a=0 \\ \\ \Rightarrow\ 5a=-2b-8 \\ \\ \Rightarrow\ a=-\frac{2b+8}{5} \\ \\ \Rightarrow\ a=-\frac{2(b+4)}{5} \\ \\ \Rightarrow\ a=-\frac{2}{5}\ (b+4)$

I think this may be the right answer. Hope this helps you.

Thank you...