Problem

Given that $x = \dfrac{3}{8} + \dfrac{7}{8}i$ is a root of the equation

$4x^3 - 19x^2 + px + q = 0$

(a) write down the other complex root of the equation.

Given that $x = 4$ is also a root of the equation,

(b) find the value of $p$ and the value of $q$.