Edexcel F1 2015 June — Question 1

Exam BoardEdexcel
ModuleF1 (Further Pure Mathematics 1)
Year2015
SessionJune
TopicFactor & Remainder Theorem
TypePolynomial identity or expansion

  1. Given that
$$2 z ^ { 3 } - 5 z ^ { 2 } + 7 z - 6 \equiv ( 2 z - 3 ) \left( z ^ { 2 } + a z + b \right)$$ where \(a\) and \(b\) are real constants,
  1. find the value of \(a\) and the value of \(b\).
  2. Given that \(z\) is a complex number, find the three exact roots of the equation $$2 z ^ { 3 } - 5 z ^ { 2 } + 7 z - 6 = 0$$