Edexcel F1 2021 October — Question 4

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2021
SessionOctober
TopicRoots of polynomials

4. $$f ( z ) = 2 z ^ { 3 } - z ^ { 2 } + a z + b$$ where \(a\) and \(b\) are integers. The complex number \(- 1 - 3 \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
  1. Write down another complex root of this equation.
  2. Determine the value of \(a\) and the value of \(b\).
  3. Show all the roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.
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