7.
\(f ( z ) = z ^ { 3 } + z ^ { 2 } + p z + q\), where \(p\) and \(q\) are real constants.
The equation \(f ( z ) = 0\) has roots \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\).
When plotted on an Argand diagram, the points representing \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\) form the vertices of a triangle of area 35. Given that \(z _ { 1 } = 3\), find the values of \(p\) and \(q\).
[0pt] [BLANK PAGE]