AQA FP1 2005 January — Question 1

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2005
SessionJanuary
TopicRoots of polynomials

1 The equation $$x ^ { 2 } - 5 x - 2 = 0$$ has roots \(\alpha\) and \(\beta\).
  1. Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
  2. Find the value of \(\alpha ^ { 2 } \beta + \alpha \beta ^ { 2 }\).
  3. Find a quadratic equation which has roots $$\alpha ^ { 2 } \beta \quad \text { and } \quad \alpha \beta ^ { 2 }$$