CAIE P2 2004 June — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2004
SessionJune
TopicFactor & Remainder Theorem
TypeStandard verify, factorise, solve

3 The cubic polynomial \(2 x ^ { 3 } + a x ^ { 2 } - 13 x - 6\) is denoted by \(\mathrm { f } ( x )\). It is given that ( \(x - 3\) ) is a factor of \(\mathrm { f } ( x )\).
  1. Find the value of \(a\).
  2. When \(a\) has this value, solve the equation \(\mathrm { f } ( x ) = 0\).