CAIE P3 2013 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2013
SessionNovember
TopicFactor & Remainder Theorem
TypeSingle unknown from factor condition

3 The polynomial \(\mathrm { f } ( x )\) is defined by $$f ( x ) = x ^ { 3 } + a x ^ { 2 } - a x + 14$$ where \(a\) is a constant. It is given that ( \(x + 2\) ) is a factor of \(\mathrm { f } ( x )\).
  1. Find the value of \(a\).
  2. Show that, when \(a\) has this value, the equation \(\mathrm { f } ( x ) = 0\) has only one real root.