CAIE P3 2011 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionNovember
TopicFactor & Remainder Theorem
TypeFind constants with divisibility condition

3 The polynomial \(x ^ { 4 } + 3 x ^ { 3 } + a x + 3\) is denoted by \(\mathrm { p } ( x )\). It is given that \(\mathrm { p } ( x )\) is divisible by \(x ^ { 2 } - x + 1\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, find the real roots of the equation \(\mathrm { p } ( x ) = 0\).