The answers are p=3 q=2
I don't know the steps, pls help me
Thanks.
Note that $\displaystyle \frac{\alpha}{2}$ is a root of $\displaystyle 2x^2+x+1$. This means:
$\displaystyle 2\left(\frac{\alpha}{2}\right)^2+\frac{\alpha}{2}+ 1=0$
$\displaystyle \frac{\alpha^2}{2}+\frac{\alpha}{2}+1=0$
$\displaystyle \frac{\alpha^2}{2}=-\frac{\alpha}{2}-1$
$\displaystyle \alpha^2=-\alpha-2$
Use this, along with $\displaystyle \alpha^4=(\alpha^2)^2$, to get your result.
--Kevin C.