6 The equation
$$2 x ^ { 2 } + 3 x - 6 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the value of \(\alpha + \beta\) and the value of \(\alpha \beta\).
- Hence show that \(\alpha ^ { 3 } + \beta ^ { 3 } = - \frac { 135 } { 8 }\).
- Find a quadratic equation, with integer coefficients, whose roots are \(\alpha + \frac { \alpha } { \beta ^ { 2 } }\) and \(\beta + \frac { \beta } { \alpha ^ { 2 } }\).