Question 90355
Any rational zero can be found through this equation


*[Tex \LARGE Roots=\frac{p}{q}] where p and q are the factors of the last and first coefficients



So let's list the factors of 5


*[Tex \LARGE p=\pm1, \pm5]


Now let's list the factors of 4


*[Tex \LARGE q=\pm1, \pm2, \pm4]


Now let's divide each factor of the last coefficient by each factor of the first coefficient



*[Tex \LARGE \frac{1}{1}, \frac{1}{2}, \frac{1}{4}, \frac{5}{1}, \frac{5}{2}, \frac{5}{4}, \frac{-1}{1}, \frac{-1}{2}, \frac{-1}{4}, \frac{-5}{1}, \frac{-5}{2}, \frac{-5}{4}]


Now simplify


These are all the possible zeros of the function


*[Tex \LARGE 1, \frac{1}{2}, \frac{1}{4}, 5, \frac{5}{2}, \frac{5}{4}, -1, \frac{-1}{2}, \frac{-1}{4}, -5, \frac{-5}{2}, \frac{-5}{4}]