Problem

(a) Express $4x^2 - 24x + p$ in the form $a(x + b)^2 + c$, where $a$ and $b$ are integers and $c$ is to be given in terms of the constant $p$.

(b) Hence or otherwise find the set of values of $p$ for which the equation $4x^2 - 24x + p = 0$ has no real roots.