Four tangent angles from a quadratic
8 written marks
Solve \(3\tan^2x+2\tan x-1=0\) on \(0\le x\lt 2\pi\).
Part a · 2 marks
Factor the quadratic in \(u=\tan x\) and find its two ratio roots.
Part b · 4 marks
Give all solutions exactly using inverse notation, and then numerically to 3 decimal places.
Part c · 2 marks
Without listing them, state the number of distinct solutions on \(0\le x\lt 4\pi\) and justify your answer.
Complete-answer checking, worked solutions and indicative written criteria.
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