1 The quadratic equation
$$3 x ^ { 2 } - 6 x + 2 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the numerical values of \(\alpha + \beta\) and \(\alpha \beta\).
- Expand \(( \alpha + \beta ) ^ { 3 }\).
- Show that \(\alpha ^ { 3 } + \beta ^ { 3 } = 4\).
- Find a quadratic equation with roots \(\alpha ^ { 3 }\) and \(\beta ^ { 3 }\), giving your answer in the form \(p x ^ { 2 } + q x + r = 0\), where \(p , q\) and \(r\) are integers.