6.
$$\mathrm { f } ( z ) = 3 z ^ { 3 } + p z ^ { 2 } + 57 z + q$$
where \(p\) and \(q\) are real constants.
Given that \(3 - 2 \sqrt { 2 } \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- show all the roots of \(\mathrm { f } ( z ) = 0\) on a single Argand diagram,
- find the value of \(p\) and the value of \(q\).
[0pt]
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