OCR FP1 2014 June — Question 5

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicRoots of polynomials

5 The cubic equation \(2 x ^ { 3 } + 3 x + 3 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
  1. Use the substitution \(x = u + 2\) to find a cubic equation in \(u\).
  2. Hence find the value of \(\frac { 1 } { \alpha - 2 } + \frac { 1 } { \beta - 2 } + \frac { 1 } { \gamma - 2 }\).