The right answer is b) to determine where the zeros are for F(x)
Sign chart is very useful to determine where the function is positive or negative. So, a rational function must be entirely positive or entirely negative between two consecutive zeros. This means that if you put in order the real zeros of a rational function, they divide the real number line into intervals in which the function has no sign changes. In other words, if the function is continuous in some interval, then between every change in sign there will be a zero of the rational function.
