Gauss-Lucas theorem

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