How do you create a polynomial with Degree 4, 2 Positive real zeros, 0 negative real zeros, 2 complex zeros?
Any polynomial which factors to the form
will satisfy the given conditions.
A simple way to creative a polynomial with certain desired zeros is to write it first in its factored form. For example, in this case, let's make a polynomial with the zeros
Note that the solutions to
Thus we know that
While the above works,