Edexcel F1 2016 June — Question 8

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicRoots of polynomials

8. $$f ( z ) = z ^ { 4 } + 6 z ^ { 3 } + 76 z ^ { 2 } + a z + b$$ where \(a\) and \(b\) are real constants. Given that \(- 3 + 8 \mathrm { i }\) is a complex root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  1. write down another complex root of this equation.
  2. Hence, or otherwise, find the other roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  3. Show on a single Argand diagram all four roots of the equation \(f ( z ) = 0\)