CAIE P2 2003 June — Question 2

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2003
SessionJune
TopicPolynomial Division & Manipulation

2 The polynomial \(x ^ { 4 } - 9 x ^ { 2 } - 6 x - 1\) is denoted by \(\mathrm { f } ( x )\).
  1. Find the value of the constant \(a\) for which $$f ( x ) \equiv \left( x ^ { 2 } + a x + 1 \right) \left( x ^ { 2 } - a x - 1 \right)$$
  2. Hence solve the equation \(\mathrm { f } ( x ) = 0\), giving your answers in an exact form.