Edexcel F1 2015 June — Question 3

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2015
SessionJune
TopicRoots of polynomials

3. It is given that \(\alpha\) and \(\beta\) are roots of the equation $$2 x ^ { 2 } - 7 x + 4 = 0$$
  1. Find the exact value of \(\alpha ^ { 2 } + \beta ^ { 2 }\)
  2. Find a quadratic equation which has roots \(\frac { \alpha } { \beta }\) and \(\frac { \beta } { \alpha }\), giving your answer in the form \(a x ^ { 2 } + b x + c = 0\), where \(a , b\) and \(c\) are integers.