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x^8 +ax^4 +1 = 0 has 4 real roots that form an arithmetic progression

Source: 2002 Estonia National Olympiad Final Round grade 11 p1

March 14, 2020

Arithmetic Progressionalgebrapolynomialarithmetic sequence

Problem Statement

Find all real parameters

a

for which the equation

x^8 +ax^4 +1 = 0

has four real roots forming an arithmetic progression.