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ax^3 - ax^2 + 9bx - b has 3 positive roots

Source: Polish MO Recond Round 1980 p4

September 9, 2024
algebrapolynomial

Problem Statement

Prove that if a a and b b are real numbers and the polynomial ax3−ax2+9bx−b ax^3 - ax^2 + 9bx - b has three positive roots, then they are equal.
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