CAIE FP1 2018 June — Question 4

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionJune
TopicRoots of polynomials
4 It is given that the equation $$x ^ { 3 } - 21 x ^ { 2 } + k x - 216 = 0$$ where \(k\) is a constant, has real roots \(a , a r\) and \(a r ^ { - 1 }\).
  1. Find the numerical values of the roots.
  2. Deduce the value of \(k\).
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