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(m-2)x^2+(m^2-4m+3)x-(6m^2-2)=0 . sum X_i^3=0

Source: 2004 Austria Beginners' Competition p3

October 4, 2022
algebrapolynomialsum of rootsQuadratic

Problem Statement

Determine the value of the parameter mm such that the equation (m−2)x2+(m2−4m+3)x−(6m2−2)=0(m-2)x^2+(m^2-4m+3)x-(6m^2-2)=0 has real solutions, and the sum of the third powers of these solutions is equal to zero.
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