Talk:2013 AIME II Problems/Problem 12

This solution doesn't seem right to me.

There are way more than 4 polynomials with all real roots. (z-13)(z-13)(z-13); (z-13)(z-13)(z-20); (z-13)(z-13)(z+13); (z-13)(z-13)(z+20)....

Also, if in the first part the other two roots are supposed to be non-real, then the inequalities should be strict.