1.
$$f ( z ) = 2 z ^ { 3 } - 4 z ^ { 2 } + 15 z - 13$$
Given that \(\mathrm { f } ( z ) \equiv ( z - 1 ) \left( 2 z ^ { 2 } + a z + b \right)\), where \(a\) and \(b\) are real constants,
- find the value of \(a\) and the value of \(b\).
- Hence use algebra to find the three roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)