Reducibility over a certain field.
I am new to field theory. How can I show that $X^4+X^2+1$ has no roots in $F_2[X]/(X^3+X+1)$? All I know at this moment is that it is reducible over $F_2[X]/(X^3+X+1)$ as $X^4+X^2+1=(X^2+X+1)^2$. How to proceed with this problem?