1. $$f ( z ) = z ^ { 3 } + p z ^ { 2 } + q z - 15$$ where \(p\) and \(q\) are real constants.
Given that the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) has roots $$\alpha , \frac { 5 } { \alpha } \text { and } \left( \alpha + \frac { 5 } { \alpha } - 1 \right)$$

1. solve completely the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
2. Hence find the value of \(p\).