Edexcel FP1 2018 June — Question 1

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicRoots of polynomials

1. $$f ( z ) = 2 z ^ { 3 } - 4 z ^ { 2 } + 15 z - 13$$ Given that \(\mathrm { f } ( z ) \equiv ( z - 1 ) \left( 2 z ^ { 2 } + a z + b \right)\), where \(a\) and \(b\) are real constants,
  1. find the value of \(a\) and the value of \(b\).
  2. Hence use algebra to find the three roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)