Question

Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2pi ).

Answer 1

2cos^2x+cosx-1 = 0

2cos^2x + 2cosx - cosx - 1 = 0

(2cos^2x + 2cosx) - (cosx + 1) = 0

2cosx(cosx + 1) - 1(cosx + 1) = 0

(cosx + 1)(2cosx - 1) = 0

cosx+1 = 0 or 2cosx-1 = 0

cosx+1 = 0 gives cosx = -1, x = PI

2cosx-1 = 0 gives cosx = 1/2, x = PI/3 or x = 5PI/3

answer: x = PI/3 or x = PI or x = 5PI/3