fundamental theorem of algebra result
This leads to the following theorem:
Proof The non-constant polynomial has one root, . Next, assume that a polynomial of degree has roots.
The polynomial of degree has then by the fundamental theorem of algebra a root . With polynomial division we find the unique polynomial such that . The original equation has then roots. By induction, every non-constant polynomial of degree has exactly roots.
For example, has four roots, .
|Title||fundamental theorem of algebra result|
|Date of creation||2013-03-22 14:22:01|
|Last modified on||2013-03-22 14:22:01|
|Last modified by||rspuzio (6075)|