Question

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

Answer 1

So is the answer -1/4 or -6/5?

Answer 2

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