Fundamental Theorem of Algebra: What are two roots for $x^2$?

Polynomial $x^2$ only has the root $(0,0)$, but doesn't that go against the fundamental theorem of algebra?

And if both roots are zero, then does the FToA say we can have roots that are the same number? If so wouldn't it be more appropriate to say any degree polynomial has at most $N$ roots?

Consider $x^2 -3x + 2 = 0$ It factorizes as $(x-1)(x-2) = 0$ and so has two clearly distinct roots $x = 1$ and $x = 2$.

Now consider $x^2 -2x +1 = 0$. It factorizes as $(x-1)(x-1) = 0$ In this case there are two factors which are zero if $x = 1$, so the root $x=1$ is considered to repeat (with "multiplicity" 2).

Now look at $x^2 = 0$. It factorizes as $x.x = 0$, or if it makes it clearer, $(x-0)(x-0) = 0$. Here the root $x = 0$ occurs twice, i.e. with multiplicity 2.

FtoA says that for a polynomial of degree n, there are n (some, possibly complex) roots if you include the multiplicity. This is perhaps more clearly expressed that a polynomial $p_n(x)$ will factorize as $(x-c_1)(x-c_2)....(x-c_n)$ where the $c_i$'s can be repeated and can be zero.