Problem

5. $f(x) = (9x^2 + d)(x^2 - 8x + (10d + 1))$

where $d$ is a positive constant.

(a) Find the four roots of $f(x)$ giving your answers in terms of $d$.

Given $d = 4$

(b) Express these four roots in the form $a + ib$, where $a, b \in \mathbb{R}$.

(c) Show these four roots on a single Argand diagram.