1 The equation
$$x ^ { 2 } - 5 x - 2 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
- Find the value of \(\alpha ^ { 2 } \beta + \alpha \beta ^ { 2 }\).
- Find a quadratic equation which has roots
$$\alpha ^ { 2 } \beta \quad \text { and } \quad \alpha \beta ^ { 2 }$$