Fundamental theorem of algebra applied to $y=x^2$ The fundamental theorem of algebra seems to indicate that there should be two roots for $y=x^2;$ however, applying the quadratic formula leads to just $0.$ Considering that $+0$ and $-0$ make no sense, what is the reasoning behind this superficial contradiction?

I don't know what exact statement of the Fundamental Theorem of Algebra you're using. The Fundamental Theorem of Algebra guarantees at least one root. Sometimes you'll see it stated that for a polynomial degree $n$, there are $n$ roots (some with multiplicity), but multiplicity is defined precisely by how many times the factor $(x-\lambda)$ is repeated in factorization of the polynomial. In this case, $0$ is a root of multiplicity $2$ because $x^2 = (x-0)(x-0)$.
