AQA FP1 2010 June — Question 8

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicRoots of polynomials

8 The quadratic equation $$x ^ { 2 } - 4 x + 10 = 0$$ has roots \(\alpha\) and \(\beta\).
  1. Write down the values of \(\alpha + \beta\) and \(\alpha \beta\).
  2. Show that \(\frac { 1 } { \alpha } + \frac { 1 } { \beta } = \frac { 2 } { 5 }\).
  3. Find a quadratic equation, with integer coefficients, which has roots \(\alpha + \frac { 2 } { \beta }\) and \(\beta + \frac { 2 } { \alpha }\).