AQA FP2 2009 June — Question 3

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
Year2009
SessionJune
TopicRoots of polynomials

3 The cubic equation $$z ^ { 3 } + p z ^ { 2 } + 25 z + q = 0$$ where \(p\) and \(q\) are real, has a root \(\alpha = 2 - 3 \mathrm { i }\).
  1. Write down another non-real root, \(\beta\), of this equation.
  2. Find:
    1. the value of \(\alpha \beta\);
    2. the third root, \(\gamma\), of the equation;
    3. the values of \(p\) and \(q\).