CAIE FP1 2017 November — Question 4

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2017
SessionNovember
TopicRoots of polynomials

4 The cubic equation \(2 x ^ { 3 } - 3 x ^ { 2 } + 4 x - 10 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
  1. Find the value of \(( \alpha + 1 ) ( \beta + 1 ) ( \gamma + 1 )\).
  2. Find the value of \(( \beta + \gamma ) ( \gamma + \alpha ) ( \alpha + \beta )\).