Edexcel F1 2014 June — Question 6

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicRoots of polynomials

6. It is given that \(\alpha\) and \(\beta\) are roots of the equation \(3 x ^ { 2 } + 5 x - 1 = 0\)
  1. Find the exact value of \(\alpha ^ { 3 } + \beta ^ { 3 }\)
  2. Find a quadratic equation which has roots \(\frac { \alpha ^ { 2 } } { \beta }\) and \(\frac { \beta ^ { 2 } } { \alpha }\), giving your answer in the form \(a x ^ { 2 } + b x + c = 0\), where \(a\), \(b\) and \(c\) are integers.