Edexcel CP1 2020 June — Question 1

Exam BoardEdexcel
ModuleCP1 (Core Pure 1)
Year2020
SessionJune
TopicComplex Numbers Arithmetic
TypeGiven two complex roots, find all roots

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