Question 1123325
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The general idea is this theorem of High Algebra (of the theory of symmetric functions):


<pre>
    Every symmetric function of the roots of a polynomial is (= can be presented as) the function of the coefficients of the polynomial.
</pre>


The rest is just technique.  &nbsp;&nbsp;// &nbsp;&nbsp;Concretely, &nbsp;for your symmetric function, &nbsp;implementation of this idea might be technically 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;complicated and time consuming, and what is even worst - you will learn nothing useful from it.


<pre>
    By the way, from your post, the symmetric function is simply unreadable, so it does not leave me any possibility to implement this technique

    even would I want to do it - but I don't want.
</pre>


You can find some relevant examples in my lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-functions-of-roots-of-a-square-equation.lesson>HOW TO evaluate functions of roots of a square equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/evaluation/HOW-TO-evaluate-functions-of-roots-of-a-cubic-and-quartic-equation.lesson>HOW TO evaluate functions of roots of a cubic and quartic equation</A>

in this site.


From these lessons, you will be able to see and to learn how this idea really works.