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4 roots in arithmetic progression for x^4-(3n+2)x^2+n^2=0

Source: Mathematics Regional Olympiad of Mexico West 2020 P5

September 10, 2022
arithmetic sequencealgebra

Problem Statement

Determine the values that nn can take so that the equation in x x x4−(3n+2)x2+n2=0 x^4-(3n+2)x^2+n^2=0 has four different real roots x1 x_1, x2x_2, x3x_3 and x4x_4 in arithmetic progression. That is, they satisfy that x4−x3=x3−x2=x2−x1x_4-x_3=x_3-x_2=x_2-x_1
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