View source for Gauss-Lucas theorem

''Gauss theorem''

Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g110/g110080/g1100801.png" /> be a complex polynomial, i.e., <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g110/g110080/g1100802.png" />. Then the zeros of the derivative <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g110/g110080/g1100803.png" /> are inside the convex polygon spanned by the zeros of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/g/g110/g110080/g1100804.png" />.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E. Hille,   "Analytic function theory" , '''1''' , Chelsea, reprint  (1982)  pp. 84</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  P. Henrici,   "Applied and computational complex analysis" , '''I''' , Wiley, reprint  (1988)  pp. 463ff</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  B.J. Lewin,   "Nullstellenverteilung ganzer Funktionen" , Akademie Verlag  (1962)  pp. 355</TD></TR></table>