10 The roots of the equation
$$x ^ { 3 } - 9 x ^ { 2 } + 27 x - 29 = 0$$
are denoted by \(\alpha , \beta\) and \(\gamma\), where \(\alpha\) is real and \(\beta\) and \(\gamma\) are complex.
- Write down the value of \(\alpha + \beta + \gamma\).
- It is given that \(\beta = p + \mathrm { i } q\), where \(q > 0\). Find the value of \(p\), in terms of \(\alpha\).
- Write down the value of \(\alpha \beta \gamma\).
- Find the value of \(q\), in terms of \(\alpha\) only.