Checkpoint: The FUNdamental Theorem of Algebra Solution
Determine if a is greater than or less than zero, and the number of real and non-real, complex roots for the sketch of a 3rd degree polynomial.
a > 0
There is one real root, and 2 non-real, complex roots.
Note
Q: How is it possible that a 3rd degree polynomial only has one real root?
A: The two other roots are non-real, complex roots (or a non-real, complex conjugate pair).
Q: Will you ever have one non-real, complex root? Explain.
A: No, non-real, complex roots always occur in conjugate pairs.