The question I am trying to solve is this:
$4 x^2 - 3 x - 3 = 0$ has roots $p, q$. Find all quadratic equations with roots $p^3$ and $q^3$.
I was able to answer this question by simply finding the roots of the equation using the quadratic formula ($p = -0.5687...$ and $q = 1.3187...$), cubing it, and then plugging it in as $a(x - p)(x - q)$.
This seems to work, however is quite ugly, and is not exact.
The correct answer, according to my textbook, is $a(64 x^2 - 135 x - 27)$, but I can't work out how it got that answer.