If $f(x)=2 x^4-13 x^2+a x+b$ is divisible by $x^2-3 x+2$, then $(a, b)$ is equal to
If $f(x)=2 x^4-13 x^2+a x+b$ is divisible by $x^2-3 x+2$, then $(a, b)$ is equal to
$(-9,-2)$
$(6, 4)$
$(9, 2)$
$(2, 9)$
Solution
Given, $f(x)=2 x^4-13 x^2+a x+b$ is divisible by
$\begin{aligned}
& (x-2)(x-1) . \\
& \therefore \quad f(2)=2(2)^4-13(2)^2+a(2)+b=0
\end{aligned}$
On solving Eqs. (i) and (ii), we get
$a=9, b=2$
