Putnam 1941 A1

Prove that the polynomial $(a-x)^6 -3a(a-x)^5 +\frac{5}{2} a^2 (a-x)^4 -\frac{1}{2} a^4 (a-x)^2$ takes only negative values for $0<x<a$ .

Dataset text AI-MO AoPS. Quoted with source.

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