Question 980228
{{{system(p+q=-1,pq=-2)}}}
{{{q=-2/p}}}


{{{p-2/p=-1}}}
{{{p^2-2=-p}}}
{{{p^2+p-2=0}}}
{{{(p-1)(p+2)=0}}}

If p=1, then q=-2.
These must be the roots.


The polynomial would come in factored form as  {{{(x-1)(x+2)(x-sqrt(3))(x+sqrt(3))}}}.  You can simplify and put into general form.