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
, 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?