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2014 Guts #12: Find the Monic Polynomial

Source:

April 20, 2014
algebrapolynomialquadraticsgeometry3D geometry

Problem Statement

Find a nonzero monic polynomial P(x)P(x) with integer coefficients and minimal degree such that P(1−23+43)=0P(1-\sqrt[3]2+\sqrt[3]4)=0. (A polynomial is called <spanclass=′latex−italic′>monic</span><span class='latex-italic'>monic</span> if its leading coefficient is 11.)
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