Question

what is the solution to 6cos^2 x + 5cos x + 1 = 0?

Answer 1

6cos^2x+5cosx+1=0:

Using the quadratic solution, first let y = cosx; then, 6y^2 + 5y + 1 = 0

and y = (- 5 + [25 - 4*6]) / (2*6) = (- 5 + 1) / 12 and also, y = (- 5 -1]) / 12

Hence, y = - 1/3 and y = - 1/2.

Now, cosx = - 1/3 and -1/2, so . . .

x = 109.47, 250.53, 120, and 240 degrees.