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Lösung 3.4:7b

Aus Online Mathematik Brückenkurs 2

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Version vom 10:53, 11. Mär. 2009

According to the factor theorem, a polynomial that has the zeros −1+i and −1−i must contain the factors z−(−1+i) and z−(−1−i). An example of such a polynomial is

(z−(−1+i))(z−(−1−i))=z2+2z+2.


Note: If one wants to have all the polynomials which have only these zeros, the answer is

C(z+1−i)m(z+1+i)n

where C is a non-zero constant and m and n are positive integers.

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.4:7b“