OCR FP1 2006 June — Question 10

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJune
TopicRoots of polynomials

10 The cubic equation \(x ^ { 3 } - 2 x ^ { 2 } + 3 x + 4 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
  1. Write down the values of \(\alpha + \beta + \gamma , \alpha \beta + \beta \gamma + \gamma \alpha\) and \(\alpha \beta \gamma\). The cubic equation \(x ^ { 3 } + p x ^ { 2 } + 10 x + q = 0\), where \(p\) and \(q\) are constants, has roots \(\alpha + 1 , \beta + 1\) and \(\gamma + 1\).
  2. Find the value of \(p\).
  3. Find the value of \(q\).