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Roots of some cubics

Source: Kvant Magazine No. 3 2023 M2738

January 9, 2024
algebraroots

Problem Statement

The real numbers a1,a2,a3a_1,a_2,a_3 and bb{} are given. The equation (x−a1)(x−a2)(x−a3)=b(x-a_1)(x-a_2)(x-a_3)=bhas three distinct real roots, c1,c2,c3.c_1,c_2,c_3. Determine the roots of the equation (x+c1)(x+c2)(x+c3)=b.(x+c_1)(x+c_2)(x+c_3)=b.Proposed by A. Antropov and K. Sukhov
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