Question

Find all exact solution of cos2x+3cosx+2=0 that are in interval [0, 2pi)

Answer 1

irst, use cos2x = 2cos^2x - 1

3(2cos^2x - 1) + cosx + 2 = 0
6cos^2x - 3 + cosx + 2 = 0
6cos^2x + cosx - 1 = 0
(3 cosx - 1)(2 cosx + 1) = 0
3cosx - 1=0 or 2cosx + 1=0
cosx = 1/3 or cosx = -1/2
x = 70.5, 289.5 or x = 120, 240