- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
$$\mathrm { f } ( z ) = 4 z ^ { 3 } + p z ^ { 2 } - 24 z + 108$$
where \(p\) is a constant.
Given that - 3 is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- determine the value of \(p\)
- using algebra, solve \(\mathrm { f } ( \mathrm { z } ) = 0\) completely, giving the roots in simplest form,
- determine the modulus of the complex roots of \(\mathrm { f } ( \mathrm { z } ) = 0\)
- show the roots of \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.