2 The cubic equation
$$x ^ { 3 } + p x ^ { 2 } + q x + r = 0$$
where \(p , q\) and \(r\) are real, has roots \(\alpha , \beta\) and \(\gamma\).
- Given that
$$\alpha + \beta + \gamma = 4 \quad \text { and } \quad \alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 20$$
find the values of \(p\) and \(q\).
- Given further that one root is \(3 + \mathrm { i }\), find the value of \(r\).