Relationship between discriminant and coefficients of a quadratic function

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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?

P.S.
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.