Many conclusions here but would you want your students to know why 'a' MUST EQUAL 3 and 'b' MUST EQUAL -2.
So what's the BIG IDEA here? Is this really "Fundamental"? Where is it in the Common Core?
So if a polynomial equation of "degree" n has more than n solutions, what exactly does that imply? Any restrictions on the coefficients? And what does this have to do with an identity?
For me, it's critical that we don't see these problems as curiosities or challenges designed for only the accelerated groups or the mathletes.