Find zeroes from polynomial and apply them to an equation

Question

If $a$ and $b$ are the zeroes of $x^2+px+q$ then find the value of $$((a/b)+2)((b/a)+2)$$

Answer 1

$$((a/b)+2)((b/a)+2)= 1+a/b+b/a+4 = 5+{a^2+b^2\over ab} = 3+{(a+b)^2\over ab}= 3+{p^2\over q}$$