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no fo real roots of P'(x)^2 -2P(x)P''(x) = 0 if P has 3 real distinct

Source: 1988 Swedish Mathematical Competition p4

March 28, 2021
polynomialalgebraanalysis

Problem Statement

A polynomial P(x)P(x) of degree 33 has three distinct real roots. Find the number of real roots of the equation P′(x)2−2P(x)P′′(x)=0P'(x)^2 -2P(x)P''(x) = 0.
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