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Gauss-Lucas theorem

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Gauss theorem

Let $f(z)$ be a complex polynomial, i.e., $f(z)\in\mathbf C[z]$. Then the zeros of the derivative $f'(z)$ are inside the convex polygon spanned by the zeros of $f(z)$.

References

[a1] E. Hille, "Analytic function theory" , 1 , Chelsea, reprint (1982) pp. 84
[a2] P. Henrici, "Applied and computational complex analysis" , I , Wiley, reprint (1988) pp. 463ff
[a3] B.J. Lewin, "Nullstellenverteilung ganzer Funktionen" , Akademie Verlag (1962) pp. 355
How to Cite This Entry:
Gauss-Lucas theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gauss-Lucas_theorem&oldid=22495
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article