OCR FP1 2012 June — Question 6

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
TopicRoots of polynomials

6 The quadratic equation \(2 x ^ { 2 } + x + 5 = 0\) has roots \(\alpha\) and \(\beta\).
  1. Use the substitution \(x = \frac { 1 } { u + 1 }\) to obtain a quadratic equation in \(u\) with integer coefficients.
  2. Hence, or otherwise, find the value of \(\left( \frac { 1 } { \alpha } - 1 \right) \left( \frac { 1 } { \beta } - 1 \right)\).