OCR FP1 2009 June — Question 5

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJune
TopicRoots of polynomials

5 The cubic equation \(x ^ { 3 } + 5 x ^ { 2 } + 7 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
  1. Use the substitution \(x = \sqrt { u }\) to find a cubic equation in \(u\) with integer coefficients.
  2. Hence find the value of \(\alpha ^ { 2 } \beta ^ { 2 } + \beta ^ { 2 } \gamma ^ { 2 } + \gamma ^ { 2 } \alpha ^ { 2 }\).