OCR FP1 2016 June — Question 3

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2016
SessionJune
TopicRoots of polynomials

3 The quadratic equation \(k x ^ { 2 } + x + k = 0\) has roots \(\alpha\) and \(\beta\).
  1. Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
  2. Find the value of \(\left( \alpha + \frac { 1 } { \alpha } \right) \left( \beta + \frac { 1 } { \beta } \right)\) in terms of \(k\).