So far I have not been able to find a book on my level about the theory of polynomial equations. I am taking a class on "advanced algebra" and one of the units is theory of equations, I'd like to learn more about it since I find it interesting. We learn about the following things: Fundamental Theorem of Algebra (without proof), Descartes' rule of signs, Bolzano's Theorem, Approximation o irrational roots by Ruffini-Horner, and also a bunch of transformation for polynomial equations, for example, given a polynomial equation $f(x) = 0$, transform it into a polynomial equation that has the same roots, but now all roots have multiplicity one. To achieve this we find the greatest common divisor of $f(x)$ and its first derivative, and divide $f(x)$ by the result. I would like to learn about more transformations to polynomial equations like that. We don't see this in class but I would also like to learn about Sturm's Theorem while I am at it.
So yeah, my level is pretty much just calculus, I haven't taken an abstract algebra class or anything like that, and I am starting to think I might need to since I can't find a single book that treats polynomial equations at this level, like what I am seeing in class, but in a book.