Question:
Let $ \ 2 $ be the only root of the following quadratic equation $ \ x^2 + px + q = 0$ with integer coefficients $ \ p$ and $ \ q$. Determine the numeral values for both $ \ p $ and $ \ q$.
My attempt:
Since the equation has only one root $ \ b^2 -4ac = 0$. So, $ \ p^2 - 4q = 0$. Now should I find $ p$ and $ \ q$ that satisfy this?