- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Given that \(x = 2 + 3 \mathrm { i }\) is a root of the equation
$$2 x ^ { 4 } - 8 x ^ { 3 } + 29 x ^ { 2 } - 12 x + 39 = 0$$
- write down another complex root of this equation.
- Use algebra to determine the other 2 roots of the equation.
- Show all 4 roots on a single Argand diagram.