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On the equation x^4 + ax^3 + bx^2 + ax + 1 = 0

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August 29, 2010
algebrapolynomialalgebra unsolved

Problem Statement

Consider the equation x4+ax3+bx2+ax+1=0x^4 + ax^3 + bx^2 + ax + 1 = 0 with real coefficients a,ba, b. Determine the number of distinct real roots and their multiplicities for various values of aa and bb. Display your result graphically in the (a,b)(a, b) plane.
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