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x^3 -2p(p+1)x^2+(p^4 +4p^3 -1)x-3p^3, roots are sidelengths

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1995 p6

February 20, 2020
sidelenghtspolynomialalgebraparameter

Problem Statement

Find all real parameters pp for which the equation x3−2p(p+1)x2+(p4+4p3−1)x−3p3=0x^3 -2p(p+1)x^2+(p^4 +4p^3 -1)x-3p^3 = 0 has three distinct real roots which are sides of a right triangle.
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