2 The cubic equation \(3 z ^ { 3 } + p z ^ { 2 } + 17 z + q = 0\), where \(p\) and \(q\) are real, has a root \(\alpha = 1 + 2 \mathrm { i }\).
- Write down the value of another non-real root, \(\beta\), of this equation.
- Hence find the value of \(\alpha \beta\).
- Find the value of the third root, \(\gamma\), of this equation.
- Find the values of \(p\) and \(q\).