Edexcel F1 2023 June — Question 2

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2023
SessionJune
TopicComplex numbers 2

  1. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Given that \(x = 2 + 3 \mathrm { i }\) is a root of the equation $$2 x ^ { 4 } - 8 x ^ { 3 } + 29 x ^ { 2 } - 12 x + 39 = 0$$
  1. write down another complex root of this equation.
  2. Use algebra to determine the other 2 roots of the equation.
  3. Show all 4 roots on a single Argand diagram.