CAIE FP1 2018 November — Question 1

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionNovember
TopicRoots of polynomials

1 The roots of the cubic equation $$x ^ { 3 } - 5 x ^ { 2 } + 13 x - 4 = 0$$ are \(\alpha , \beta , \gamma\).
  1. Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\).
  2. Find the value of \(\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 }\).