The given function is
[tex]2\cos ^2x+\cos x+15=0[/tex]Solve the equation to get:
[tex]\cos x=\frac{-1\pm\sqrt[]{1-4\ast2\ast15}}{4}=\frac{-1\pm\sqrt[]{-119}}{4}[/tex]The square root of a negative number is not real hence there are no real valued solutions
Option C is correct.
