Problem

2. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

Given that $x = 2 + 3i$ is a root of the equation

$2x^4 - 8x^3 + 29x^2 - 12x + 39 = 0$

(a) write down another complex root of this equation.

(b) Use algebra to determine the other 2 roots of the equation.

(c) Show all 4 roots on a single Argand diagram.