There are three changes of sign in the coefficients of \(p ( x )\) and no changes of sign in the coefficients of \(p ( -x )\). Thus there are either three or one positive zeros and no negative zeros. Since there must be a total of five zeros, it is either the case that there are three positive zeros and two complex zeros or it is the case that there is one positive zero and four complex zeros. The chart showing the possible distribution of zeros follows:
| Positive | \(3\) | \(1\) |
| Negative | \(0\) | \(0\) |
| Complex | \(2\) | \(4\) |