OCR MEI Further Pure Core 2021 November — Question 8

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2021
SessionNovember
TopicRoots of polynomials

8 The equation \(4 \mathrm { x } ^ { 4 } - 4 \mathrm { x } ^ { 3 } + \mathrm { px } ^ { 2 } + \mathrm { qx } - 9 = 0\), where \(p\) and \(q\) are constants, has roots \(\alpha , - \alpha , \beta\) and \(\frac { 1 } { \beta }\).
  1. Determine the exact roots of the equation.
  2. Determine the values of \(p\) and \(q\).