Edexcel F1 2018 June — Question 7

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicRoots of polynomials

7. It is given that \(\alpha\) and \(\beta\) are roots of the equation \(5 x ^ { 2 } - 4 x + 3 = 0\) Without solving the quadratic equation,
  1. find the exact value of \(\frac { 1 } { \alpha ^ { 2 } } + \frac { 1 } { \beta ^ { 2 } }\)
  2. find a quadratic equation which has roots \(\frac { 3 } { \alpha ^ { 2 } }\) and \(\frac { 3 } { \beta ^ { 2 } }\)
    giving your answer in the form \(a x ^ { 2 } + b x + c = 0\), where \(a\), \(b\) and \(c\) are integers to be found.