OCR FP1 2007 January — Question 7

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJanuary
TopicRoots of polynomials

7 The quadratic equation \(x ^ { 2 } + 5 x + 10 = 0\) has roots \(\alpha\) and \(\beta\).
  1. Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
  2. Show that \(\alpha ^ { 2 } + \beta ^ { 2 } = 5\).
  3. Hence find a quadratic equation which has roots \(\frac { \alpha } { \beta }\) and \(\frac { \beta } { \alpha }\).