Edexcel F1 2018 January — Question 2

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2018
SessionJanuary
TopicRoots of polynomials

2. $$f ( z ) = z ^ { 4 } - 6 z ^ { 3 } + 38 z ^ { 2 } - 94 z + 221$$
  1. Given that \(z = 2 + 3 i\) is a root of the equation \(f ( z ) = 0\), use algebra to find the three other roots of \(f ( z ) = 0\)
  2. Show the four roots of \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.