10 The polynomial \(\mathrm { p } ( z )\) is defined by
$$\mathrm { p } ( z ) = z ^ { 3 } + m z ^ { 2 } + 24 z + 32$$
where \(m\) is a constant. It is given that \(( z + 2 )\) is a factor of \(\mathrm { p } ( z )\).
- Find the value of \(m\).
- Hence, showing all your working, find
(a) the three roots of the equation \(\mathrm { p } ( z ) = 0\),
(b) the six roots of the equation \(\mathrm { p } \left( z ^ { 2 } \right) = 0\).