OCR MEI FP1 2007 June — Question 9

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJune
TopicRoots of polynomials

9 The cubic equation \(x ^ { 3 } + A x ^ { 2 } + B x + 15 = 0\), where \(A\) and \(B\) are real numbers, has a root \(x = 1 + 2 \mathrm { j }\).
  1. Write down the other complex root.
  2. Explain why the equation must have a real root.
  3. Find the value of the real root and the values of \(A\) and \(B\).