2012 UNCO Math Contest II Problems/Problem 11

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

$x^4-x^3-\tfrac{1}{2}x^2-\tfrac{1}{6}x+\tfrac{1}{24}$

2012 UNCO Math Contest II (Problems • Answer Key • Resources)
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2012 UNCO Math Contest II Problems/Problem 11

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