At the top of p.15 in the 3rd edition, it states: "[I]rrational roots of rational-coefficient polynomial equations must occur in conjugate radical pairs." However, this fails to account for irrational roots not of the form .

Following their line of reasoning may prove disastrous. For instance, question #17 of GR0568 asks to find the number of real roots of . Since and , there is at least one root. Moreover, that root must be irrational, as a quick application of the rational roots theorem shows. If we take PR at their word, we're forced to conclude that there are at least two zeroes. However, , so there can be at most one zero. Indeed, the answer key confirms there is exactly one.

Studying with this guide has been nothing but a crap shoot. It seems I'm only slightly more likely to learn useful information than I am to fall prey to subtle yet fatal errors. After two revisions, obvious pitfalls remain. What is going on here?