Edexcel FP1 2010 January — Question 6

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
TopicRoots of polynomials

6. Given that 2 and \(5 + 2 \mathrm { i }\) are roots of the equation $$x ^ { 3 } - 12 x ^ { 2 } + c x + d = 0 , \quad c , d \in \mathbb { R }$$
  1. write down the other complex root of the equation.
  2. Find the value of \(c\) and the value of \(d\).
  3. Show the three roots of this equation on a single Argand diagram.