Edexcel FP1 2010 June — Question 4

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicRoots of polynomials

4. $$f ( x ) = x ^ { 3 } + x ^ { 2 } + 44 x + 150$$ Given that \(\mathrm { f } ( x ) = ( x + 3 ) \left( x ^ { 2 } + a x + b \right)\), where \(a\) and \(b\) are real constants,
  1. find the value of \(a\) and the value of \(b\).
  2. Find the three roots of \(\mathrm { f } ( x ) = 0\).
  3. Find the sum of the three roots of \(\mathrm { f } ( x ) = 0\).