Edexcel FP1 Specimen — Question 8

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

8. $$\mathrm { f } ( x ) \equiv 2 x ^ { 3 } - 5 x ^ { 2 } + p x - 5 , p \in \mathbb { R }$$ Given that \(1 - 2 \mathrm { i }\) is a complex solution of \(\mathrm { f } ( x ) = 0\),
  1. write down the other complex solution of \(\mathrm { f } ( x ) = 0\),
  2. solve the equation \(\mathrm { f } ( x ) = 0\),
  3. find the value of \(p\).