1) For the factor theorem on pg. 102, what if you deal with something like bx-a. Is there a theorem that tells us that a/b is a root of the polynomial? Also, how do we know when we need to use induction for a proof (like on the proof of corollary 4.16). How can you prove that something does not have roots?
2) I am just curious when we can switch fields to get roots, like how sometimes we say a polynomial has imaginary roots?
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