OCR FP1 2013 January — Question 4

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJanuary
TopicRoots of polynomials

4 The quadratic equation \(x ^ { 2 } + x + k = 0\) has roots \(\alpha\) and \(\beta\).
  1. Use the substitution \(x = 2 u + 1\) to obtain a quadratic equation in \(u\).
  2. Hence, or otherwise, find the value of \(\left( \frac { \alpha - 1 } { 2 } \right) \left( \frac { \beta - 1 } { 2 } \right)\) in terms of \(k\).