It is given that $z=3+2\mathbf{i}$ is a root of the equation \(2{{z}^{3}}+p{{z}^{2}}+qz-65=0\

Question

It is given that $z=3+2\mathbf{i}$ is a root of the equation $2{{z}^{3}}+p{{z}^{2}}+qz-65=0$, where $p$ and $q$ are real numbers. Find the values of $p$ and $q$. [3] Without the use of a calculator, find the values of all the other roots of the equation. [3]

Accepted Answer

$p=-17$ and $q=56$; $3-2\mathbf{i}$ and $2.5$

2013 NJC P1 Q11

2013 NJC P1 Q11