Do you remember learning about the discriminant? For a quadratic equation of the form: The discriminant is equal to:

It tells us how many solutions a quadratic equation has. The discriminant can give us three results regarding the roots of an equation.

a) What are these three different results? What must the discriminant be in order to get each result? Describe what a graphed quadratic equation would look like with each result.
b) Where does the discriminant come from?
c) Use the ideas from parts A and B to prove that every quadratic polynomial has exactly two roots.