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?

The Fundamental Theorem of Algebra allows multiple roots. In this case$x=0$ counts twices so you have a root of multiplicity two. For example $y=(x-1)^3(x+3)^2$ which is a polynomial of degree $5$,has $x=1$ with multiplicity $3$ and $x=-3$ with multiplicity $2$. 
