CAIE P2 2018 June — Question 3

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2018
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
3
  1. Find the quotient when $$x ^ { 4 } - 2 x ^ { 3 } + 8 x ^ { 2 } - 12 x + 13$$ is divided by \(x ^ { 2 } + 6\) and show that the remainder is 1 .
  2. Show that the equation $$x ^ { 4 } - 2 x ^ { 3 } + 8 x ^ { 2 } - 12 x + 12 = 0$$ has no real roots.
3 (i) Find the quotient when

$$x ^ { 4 } - 2 x ^ { 3 } + 8 x ^ { 2 } - 12 x + 13$$

is divided by $x ^ { 2 } + 6$ and show that the remainder is 1 .\\

(ii) Show that the equation

$$x ^ { 4 } - 2 x ^ { 3 } + 8 x ^ { 2 } - 12 x + 12 = 0$$

has no real roots.\\

\hfill \mbox{\textit{CAIE P2 2018 Q3}}
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