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 = , 
        then it has the root  a-bi,  too.



    The other conjugate root theorem says:


        If a polynomial with rational coefficients has a root  with rational "a" and "b", 
        then it has the root , too.



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

    the root  goes in pair with the root  ;

    the root  goes in pair with the root  ;

    the root  goes in pair with the root  .


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