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a,b>=5 if ax^2-bx + c = 0 has two roots in [0, 1] (1996 Chile NMO P4)

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November 22, 2021
algebraquadraticstrinomial

Problem Statement

Let a,b,ca, b, c be naturals. The equation ax2−bx+c=0ax^2-bx + c = 0 has two roots at [0,1][0, 1]. Prove that a≥5a\ge 5 and b≥5b\ge 5.
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