Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)=2 x^{4}-13 x^{2}+a x+b$ is divisible by $\mathrm{x}^{2}-3 x+2$, then $(a, b)$ is equal to
Options:
Solution:
2597 Upvotes
Verified Answer
The correct answer is:
$(9,2)$
$$
\begin{array}{l}
f(x)=2 x^{4}-13 x^{2}+a x+b \text { is divisible by } \\
(x-2)(x-1) \\
\therefore f(2)=2(2)^{4}-13(2)^{2}+a(2)+b=0 \\
\Rightarrow 2 a+b=20...(i)
\end{array}
$$
$$
\begin{array}{l}
\text { and } f(1)=2(1)^{4}-13(1)^{2}+a+b=0 \\
\Rightarrow a+b=11...(ii)
\end{array}
$$
On solving Eqs. (i) and (ii), we get $a=9, b=2$
\begin{array}{l}
f(x)=2 x^{4}-13 x^{2}+a x+b \text { is divisible by } \\
(x-2)(x-1) \\
\therefore f(2)=2(2)^{4}-13(2)^{2}+a(2)+b=0 \\
\Rightarrow 2 a+b=20...(i)
\end{array}
$$
$$
\begin{array}{l}
\text { and } f(1)=2(1)^{4}-13(1)^{2}+a+b=0 \\
\Rightarrow a+b=11...(ii)
\end{array}
$$
On solving Eqs. (i) and (ii), we get $a=9, b=2$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.