Exercise 105 Page 405

In this case we are still dealing with a fifth degree polynomial, because we have five solutions in total. However, 3 are real and 2 are complex, which means it should only intercept the x-axis three times. We see an example of this below.

A graph that has 4 complex solutions reflects a fourth degree polynomial that does not intercept the x-axis. Since it is a fourth degree polynomial, it changes direction three times. We see an example of this below.

A graph that has 4 complex solutions and 2 real solutions has a total of 6 roots. This means the function is a sixth degree polynomial that intercepts the x-axis twice. We see an example of this below.

The degree needs to be at least as high as the number of solutions. With this information, we can determine the lowest degree.