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Putnam 1970 A2

Source: Putnam 1970

May 17, 2022
Putnamalgebrapolynomialroots

Problem Statement

Consider the locus given by the real polynomial equation Ax2+Bxy+Cy2+Dx3+Ex2y+Fxy2+Gy3=0, Ax^2 +Bxy+Cy^2 +Dx^3 +E x^2 y +F xy^2 +G y^3=0, where B2−4AC<0.B^2 -4AC <0. Prove that there is a positive number δ\delta such that there are no points of the locus in the punctured disk 0<x2+y2<δ2.0 <x^2 +y^2 < \delta^2.
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