- The quadratic equation
$$5 x ^ { 2 } - 4 x + 1 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the value of \(\alpha + \beta\) and the value of \(\alpha \beta\).
- Show that \(\frac { \alpha } { \beta } + \frac { \beta } { \alpha } = \frac { 6 } { 5 }\)
- Find a quadratic equation with integer coefficients, which has roots
$$\alpha + \frac { 1 } { \alpha } \text { and } \beta + \frac { 1 } { \beta }$$