One impossible algebraic root
8 written marks
Consider \(2\sin^2x-3\cos x=0\).
Part a · 3 marks
Rewrite this as a quadratic in \(u=\cos x\), then factor it.
Part b · 3 marks
Find all solutions for \(0\le x\lt 2\pi\), explaining any rejected ratio value.
Part c · 2 marks
Find the solution set instead on \(-\pi\le x\lt \pi\).
Complete-answer checking, worked solutions and indicative written criteria.
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