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points M(a, b), with x^4+ax+b=0, 0<=x<=1 (II Soros Olympiad 1995-96 R1 11.4)

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June 3, 2024
analytic geometryalgebra

Problem Statement

Draw on the coordinate plane a set of points M(a,b)M(a, b) such that the equation x4+ax+b=0x^4+ax+b=0 has a unique root satisfying the condition 0≤x≤10 \le x \le 1.
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