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

• A

  $(-9,-2)$
• B

  $(6, 4)$
• Correct answer
  C

  $(9, 2)$
• D

  $(2, 9)$

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 $a=9, b=2$

Hence, the correct answer is option: 'C'.