CAIE FP1 2019 November — Question 9

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2019
SessionNovember
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Mark schemeDownload PDF ↗
TopicComplex numbers 2
9
  1. Use de Moivre's theorem to show that $$\sec 6 \theta = \frac { \sec ^ { 6 } \theta } { 32 - 48 \sec ^ { 2 } \theta + 18 \sec ^ { 4 } \theta - \sec ^ { 6 } \theta }$$
  2. Hence obtain the roots of the equation $$3 x ^ { 6 } - 36 x ^ { 4 } + 96 x ^ { 2 } - 64 = 0$$ in the form sec \(q \pi\), where \(q\) is rational.
9 (i) Use de Moivre's theorem to show that

$$\sec 6 \theta = \frac { \sec ^ { 6 } \theta } { 32 - 48 \sec ^ { 2 } \theta + 18 \sec ^ { 4 } \theta - \sec ^ { 6 } \theta }$$

(ii) Hence obtain the roots of the equation

$$3 x ^ { 6 } - 36 x ^ { 4 } + 96 x ^ { 2 } - 64 = 0$$

in the form sec $q \pi$, where $q$ is rational.\\

\hfill \mbox{\textit{CAIE FP1 2019 Q9}}
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