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polynomial connection to geometry

Source: Romanian TST 1978, Day 1, P3

September 28, 2018
algebrapolynomialanalytic geometrygeometry

Problem Statement

Let P[X,Y] P[X,Y] be a polynomial of degree at most 2. 2 . If A,B,C,A′,B′,C′ A,B,C,A',B',C' are distinct roots of P P such that A,B,C A,B,C are not collinear and A′,B′,C′ A',B',C' lie on the lines BC,CA, BC,CA, respectively, AB, AB, in the planar representation of these points, show that P=0. P=0.
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