5. Given that
$$z ^ { 4 } - 6 z ^ { 3 } + 34 z ^ { 2 } - 54 z + 225 \equiv \left( z ^ { 2 } + 9 \right) \left( z ^ { 2 } + a z + b \right)$$
where \(a\) and \(b\) are real numbers,
- find the value of \(a\) and the value of \(b\).
- Hence find the exact roots of the equation
$$z ^ { 4 } - 6 z ^ { 3 } + 34 z ^ { 2 } - 54 z + 225 = 0$$
- Show your roots on a single Argand diagram.