Question

If $(x^2-3x+2)$ is a factor of $x^4-p{x}^2+q=0$, then the value of $p$ and $q$ are

• A. $-5,4$
• B. $5,4$
• C. $5,-4$
• D. $-5,-4$

Answer 1

Answer: (B)

$5,4$

$x^2-3x+2=0$ is a factor of $x^4-p{x}^2+q=0$

We have, $x^2-3x+2=0$

$\Rightarrow (x-1)(x-2)=0$

For $x=1,x^4-p{x}^2+q=0$

$\Rightarrow 1-p+q=0$ ...... $\left(i\right)$

For $x=2,16-4p+q=0$ ........ $\left(ii\right)$

On solving Eqs. $\left(i\right)$ and $\left(ii\right)$, we get $p=5,q=4$