From Förberedande kurs i matematik 2

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-	{{NAVCONTENT_START}}	+	According to the factor theorem, a polynomial that has the zeros <math>-1+i</math> and <math>-1-i</math> must contain the factors <math>z-(-1+i)</math> and <math>z-(-1-i)</math>. An example of such a polynomial is
-	<center> [[Bild:3_4_7b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>(z-(-1+i))(z-(-1-i)) = z^2+2z+2\,\textrm{.}</math>}}
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		+	Note: If one wants to have all the polynomials which have only these zeros, the answer is
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		+	{{Displayed math||<math>C(z+1-i)^m(z+1+i)^n</math>}}
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		+	where <math>C</math> is a non-zero constant and <math>m</math> and <math>n</math> are positive integers.

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Current revision

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

\displaystyle (z-(-1+i))(z-(-1-i)) = z^2+2z+2\,\textrm{.}

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

\displaystyle C(z+1-i)^m(z+1+i)^n

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