Question 1128236
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There are TWO conjugate root theorems:


    One (the most widely known) conjugate root theorems says:


        If a polynomial with real coefficients has a root a+bi with real "a" and "b",  and  i = {{{sqrt(-1)}}}, 
        then it has the root  a-bi,  too.



    The other conjugate root theorem says:


        If a polynomial with <U>rational</U> coefficients has a root {{{a+b*sqrt(c)}}} with <U>rational</U> "a" and "b", 
        then it has the root {{{a-b*sqrt(c)}}}, too.



By applying one and another conjugate root theorem to the given problem, we obtain that

    the root {{{-1+sqrt(6)}}} goes in pair with the root  {{{-1-sqrt(6)}}};

    the root {{{-2*sqrt(2)}}} goes in pair with the root  {{{2*sqrt(2)}}};

    the root {{{-3-i}}} goes in pair with the root  {{{-3+i}}}.


So, the polynomial has, in total, 6 (six; SIX) listed roots.
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Solved, answered and completed.