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2 diff. common roots for x^4 + 2ax^2 + 4bx + a^2 and x^3 + ax - b

Source: Polish MO Recond Round 1987 p4

September 9, 2024

algebrapolynomial

Problem Statement

Determine all pairs of real numbers

a, b

for which the polynomials

x^4 + 2ax^2 + 4bx + a^2

and

x^3 + ax - b

have two different common real roots.