Solution
= Solution
Real coefficients imply that the conjugate $-i$ is also a <polynomial root>. Write the remaining root as $r$. Then
$$
p(z)=2(z-2)(z-r)(z^2+1).
$$
The coefficient of $z$ in this product is $-2(2+r)$. That coefficient is zero in the specified <polynomial>, so $r=-2$. Hence the two other roots are
$$
\boxed{-i,\qquad -2.}
$$
As a check, the full <polynomial> is $2(z^2-4)(z^2+1)=2z^4-6z^2-8$, corresponding to $a=0$, $b=-6$ and $c=-8$.