Question

If $x^2+x-1$ is a factor of $x^4+p{x}^3+q{x}^2-1$ then the values of p and q can be -

Answer 1

$\Rightarrow 2p-q-3=0,p-q-3=0$

$\Rightarrow 2p-q=3,p-q=3$

$\Rightarrow 2p-q-p+q=3-3$ by soving $2p-q=3,p-q=3$

$\Rightarrow p=0$

$\Rightarrow q=p-3=0-3=-3$ using $p-q=3$

$\therefore p=0,q=-3$