1. What is the discriminant b2 − 4ac used for?

The discriminant tells how many roots there are and what type of number the roots will be.

2. Can the discriminant be negative?

Yes, and if it is, then this indicates that the quadratic equation has no, real roots.

3. Is there another way to determine the nature of the roots of a quadratic equation?

Yes, the equations could be solved, by factorising or using the quadratic formula, OR the graph of the corresponding quadratic function could be drawn and the number of roots would be determined by the number of x-intercepts of the graph.

Much easier to calculate the discriminant!