Edexcel FP1 2014 June — Question 3

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicRoots of polynomials

3. Given that 2 and \(1 - 5 \mathrm { i }\) are roots of the equation $$x ^ { 3 } + p x ^ { 2 } + 30 x + q = 0 , \quad p , q \in \mathbb { R }$$
  1. write down the third root of the equation.
  2. Find the value of \(p\) and the value of \(q\).
  3. Show the three roots of this equation on a single Argand diagram.