3 The cubic equation
$$z ^ { 3 } + p z ^ { 2 } + 25 z + q = 0$$
where \(p\) and \(q\) are real, has a root \(\alpha = 2 - 3 \mathrm { i }\).
- Write down another non-real root, \(\beta\), of this equation.
- Find:
- the value of \(\alpha \beta\);
- the third root, \(\gamma\), of the equation;
- the values of \(p\) and \(q\).