1 The quadratic equation
$$3 x ^ { 2 } - 6 x + 1 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
- Show that \(\alpha ^ { 3 } + \beta ^ { 3 } = 6\).
- Find a quadratic equation, with integer coefficients, which has roots \(\frac { \alpha ^ { 2 } } { \beta }\) and \(\frac { \beta ^ { 2 } } { \alpha }\).