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Putnam 1953 A7

Source: Putnam 1953

July 16, 2022
Putnamtrigonometrypolynomialroots

Problem Statement

Assuming that the roots of x3+px2+qx+r=0x^3 +px^2 +qx +r=0 are all real and positive, find the relation between p,q,rp,q,r which is a necessary and sufficient condition that the roots are the cosines of the angles of a triangle.
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