2025 SJI P2 Q2

Let \(z_1=2\) and \(z_2=3+\mathrm i\) be roots of the cubic equation

\[z^3+az^2+bz+c=0,\quad\text{where}\hspace{0.5em}a,b,c\in\mathbb R.\]

1. Write down the third root of the equation.[1]
2. Find the values of \(a,b\) and \(c\).[4]