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2012 UNCO Math Contest II Problems/Problem 11

Revision as of 03:24, 17 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Construct a <math>4</math>th degree polynomial <math>x^4+ax^3+bx^2+cx+d</math> that meets as many of the following conditions as you can: the sum of the roots is ...")
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Problem

Construct a $4$th degree polynomial $x^4+ax^3+bx^2+cx+d$ that meets as many of the following conditions as you can: the sum of the roots is $1$, the sum of the squares of the roots is $2$, the sum of the cubes of the roots is $3$, and the sum of the $4$th powers of the roots is $4$.


Solution

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