OCR C2 2009 January — Question 9

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
TopicFactor & Remainder Theorem
TypeTrigonometric substitution equations

9
  1. The polynomial \(\mathrm { f } ( x )\) is defined by $$\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 3 x + 3$$ Show that \(x = 1\) is a root of the equation \(\mathrm { f } ( x ) = 0\), and hence find the other two roots.
  2. Hence solve the equation $$\tan ^ { 3 } x - \tan ^ { 2 } x - 3 \tan x + 3 = 0$$ for \(0 \leqslant x \leqslant 2 \pi\). Give each solution for \(x\) in an exact form.