CAIE P3 2016 November — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionNovember
TopicFactor & Remainder Theorem
TypeFind constants with divisibility condition

4 The polynomial \(4 x ^ { 4 } + a x ^ { 2 } + 11 x + b\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(\mathrm { p } ( x )\) is divisible by \(x ^ { 2 } - x + 2\).
  1. Find the values of \(a\) and \(b\).
  2. When \(a\) and \(b\) have these values, find the real roots of the equation \(\mathrm { p } ( x ) = 0\).