Processing Math: Done

Aus Online Mathematik Brückenkurs 2

There exists a simple relation between a zero and the polynomial's factorization: z=a is a zero if and only if the polynomial contains the factor z−a . (This is the meaning of the factor theorem.)

If we are to have a polynomial with zeros at 1 2 and 4, the polynomial must therefore contain the factors z−1 z−2  and z−4 . For example,

z−1z−2z−4=z3−7z2+14z−8 

NOTE: it is possible to multiply the polynomial above by a non-zero constant and get another third-degree polynomial with the same roots.