5 The roots of the quadratic equation
$$x ^ { 2 } + 2 x - 5 = 0$$
are \(\alpha\) and \(\beta\).
- Write down the value of \(\alpha + \beta\) and the value of \(\alpha \beta\).
- Calculate the value of \(\alpha ^ { 2 } + \beta ^ { 2 }\).
- Find a quadratic equation which has roots \(\alpha ^ { 3 } \beta + 1\) and \(\alpha \beta ^ { 3 } + 1\).