part-1. i am going to show you some special of a quartic polynomial which makes it easier to solve. in future notes i will try to generalize for every quartic polynomials. 2 cases to be presented here:
case 1: consider the polynomial
i think most of you know how to factor this easily, but i am going to continue regardless.
i think this is the most general form, as going farther will simply make it more tedious.
the minus sign will have the negative root, and the positive sign the positive. second one:
we can actually simplify these two results to get our original polynomials.