Question

Let $P\left(x\right)=x^2+bx+c$, where $b$ and $c$ are integers. If $P\left(x\right)$ is a facter of both $x^4+6x^2+25$ and $3x^4+4x^2+28x+5$, then value of $P\left(1\right)$ is -

• A. $4$
• B. $8$
• C. $10$
• D. $12$

Answer 1

The correct option is A $4$

Since, $P\left(x\right)=x^2+bx+c$, where $b$ and $c$ are integers. If $P\left(x\right)$ is a facter of both $x^4+6x^2+25$ and $3x^4+4x^2+28x+5$
Therefore, $P\left(x\right)$ will be factor of $(3x^4+4x^2+28x+5)-3(x^4+6x^2+25)=-14(x^2-2x+5)$
So $P\left(x\right)=x^2-2x+5$
$P\left(1\right)=1-2+5=4$