Relationship between discriminant and coefficients of a quadratic function

enter the description of the image here

To answer question (b), the problem requires that I use the discriminant. However, I still do not understand how I would realize that I should make use of it. Can any one please explain the relationship between the two inequalities?

For those who think that I am looking for answers to a duty, I have the answer to (b), so it is not necessary to provide it.