Does the degree of a polynomial give the number of roots? I am aware of the fundamental theorem of algebra, i.e., the degree of a polynomial is the number of roots of the polynomial. For example, $x^2 - 9 = 0$ would have two solutions: $x=3$ and $x=-3$. However, sometimes I come across quadratic polynomials that only have one root, e.g., 
$$t^2 - 2 t + 1 = (t-1)(t-1) = 0$$
which only has the solution $1$, or so I think. Is there some underlying concept that I am overlooking?

Two main things overlooked as far as I can tell:


*

*Multiplicities, the number of times a root occurs.

*Complex roots, $x^2+1=0$ has no real roots, but two complex roots i, and -i.
