According to the rational root theorem, the following are potential roots of f(x) = 60x^2 - 57x - 18. which is an actual root a) -6/5 b) -1/4 c) 3 d) 6

I would immediately use synthetic division to check the four possible answers.

Is -1/4 an actual root?  Let's find out:

         
-1/4  /   60     -57     - 18
                      -15     18
       
             60      -72      0

Since there is no remainder, -1/4 IS a factor of the given polynomial, and the other factor can be found from  the coefficients 60  - 72:
                                 72
60x - 72 = 0  => x = = 6/5
                                 60