Question 113
Find all non-zero real numbers $a$, $b$, $c$ such that the following polynomial has four (not necessarily distinct) positive real roots.
$$P(x) = a x^{4} - 8a x^{3} + b x^{2} - 32c x + 16c$$
$$P(x) = a x^{4} - 8a x^{3} + b x^{2} - 32c x + 16c$$