CAIE P3 2012 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionNovember
TopicRoots of polynomials

9 The complex number \(1 + ( \sqrt { } 2 ) \mathrm { i }\) is denoted by \(u\). The polynomial \(x ^ { 4 } + x ^ { 2 } + 2 x + 6\) is denoted by \(\mathrm { p } ( x )\).
  1. Showing your working, verify that \(u\) is a root of the equation \(\mathrm { p } ( x ) = 0\), and write down a second complex root of the equation.
  2. Find the other two roots of the equation \(\mathrm { p } ( x ) = 0\).