Putnam 1970 A2

Consider the locus given by the real polynomial equation $$Ax^2 +Bxy+Cy^2 +Dx^3 +E x^2 y +F xy^2 +G y^3=0,$$ where $B^2 -4AC <0.$ Prove that there is a positive number $\delta$ such that there are no points of the locus in the punctured disk $$0 <x^2 +y^2 < \delta^2.$$