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Polynomials with common roots and coefficients

Source: Balkan MO SL 2020 A3

September 9, 2021
algebraPolynomialsAZE EGMO TST

Problem Statement

Let P(x),Q(x)P(x), Q(x) be distinct polynomials of degree 20202020 with non-zero coefficients. Suppose that they have rr common real roots counting multiplicity and ss common coefficients. Determine the maximum possible value of r+sr + s.
Demetres Christofides, Cyprus
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