Edexcel F1 2021 January — Question 2

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

  1. Given that \(x = \frac { 3 } { 8 } + \frac { \sqrt { 71 } } { 8 } \mathrm { i }\) is a root of the equation
$$4 x ^ { 3 } - 19 x ^ { 2 } + p x + q = 0$$
  1. write down the other complex root of the equation. Given that \(x = 4\) is also a root of the equation,
  2. find the value of \(p\) and the value of \(q\).