8 The quadratic equation
$$x ^ { 2 } - 4 x + 10 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
- Show that \(\frac { 1 } { \alpha } + \frac { 1 } { \beta } = \frac { 2 } { 5 }\).
- Find a quadratic equation, with integer coefficients, which has roots \(\alpha + \frac { 2 } { \beta }\) and \(\beta + \frac { 2 } { \alpha }\).