OCR MEI FP1 2006 June — Question 3

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJune
TopicRoots of polynomials

3 The cubic equation \(z ^ { 3 } + 4 z ^ { 2 } - 3 z + 1 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
  1. Write down the values of \(\alpha + \beta + \gamma , \alpha \beta + \beta \gamma + \gamma \alpha\) and \(\alpha \beta \gamma\).
  2. Show that \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 22\).