If a Polynomial $x^4+x^2+1$ is divisible by $x^2+m x+1$ and $x^2+n x+1$. Then $m+n$ is equal to (1) 2 (2) 0…
If a Polynomial $x^4+x^2+1$ is divisible by $x^2+m x+1$ and $x^2+n x+1$. Then $m+n$ is equal to
(1) 2
(2) 0
(3) 3
(4) 4
2
0
3
4
Solution
$x^4+x^2+1$ is divisible by $x^2+n x+1$ and $x^2+m x+1$
$
\therefore x^4+x^2+1=\left(x^2+m x+1\right)\left(x^2+n x+1\right)
$
equating the coefficients of $x^3$ on both sides
$
m+n=0
$