5.
$$f ( x ) = x ^ { 2 } - 6 x + 3$$
The equation \(\mathrm { f } ( x ) = 0\) has roots \(\alpha\) and \(\beta\)
Without solving the equation,
- determine the value of
$$\left( \alpha ^ { 2 } + 1 \right) \left( \beta ^ { 2 } + 1 \right)$$
- find a quadratic equation which has roots
$$\frac { \alpha } { \left( \alpha ^ { 2 } + 1 \right) } \text { and } \frac { \beta } { \left( \beta ^ { 2 } + 1 \right) }$$
giving your answer in the form \(p x ^ { 2 } + q x + r = 0\) where \(p , q\) and \(r\) are integers to be determined.