Van den Berg’s Theorem

Let Q(z)=z3+a1z2+a2z+a3=0 be a cybic in C and  z1,z2,z3 the roots denoted in the plane by the points A,B,C. The Steiner ellipse in the triangle ABC is denoted by E and F1, F2 the foci. Van den Berg’s theorem asserts that the roots of the derivate Q'(z) are the complex numbers defined in C by the points F1 and F2.

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