IMO 1986 LL SWE68

Consider the equation x4 + ax3 + bx2 + ax + 1 = 0 with real

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IMO 1986 LL SWE68

Origin: SWE

Problem

Consider the equation x4 + ax3 + bx2 + ax + 1 = 0 with real coefficients a, b. Determine the number of distinct real roots and their multiplicities for various values of a and b. Display your result graphically in the (a, b) plane.