|
Any polynomial of degree n has
n roots, some of which may be repeated. If any root is repeated, the
number of repetitions is referred to as the multiplicity of the root.
The Fundamental Theorem can be restated to say that the sum of multiplicities
for all roots of an nth degree polynomial is equal to n. The roots may
be either real or complex.
Karl Friedrich Gauss first proved
the theorem around 1798.
The proof of the theorem
made it absolutely clear that there are some numbers that can't be seen,
in the normal sense of identifying roots at the points where their graphs
crossed the x-axis. This was one of the first results in what would
eventually become known as complex number theory.
|