Compute the product of the nonreal roots of the equation $x^4+4x^3+6x^2+1004x+1001=0$.
So here is what I have done so far. I got two of the roots to be zero and 4 since $x^3(x+4)+(6x^2+1004x+1001)=0$. But for the other two roots by using the quadratic formula I get $\frac{-1004 \pm \sqrt{1004^2-24024}}{12}.$ This contest was already completed but I couldn't solve that quadratic equation during the competition. Can someone please post a easier way to solve this problem?