I'm using "only obstacle" in the same way mathematicians use the word "trivial": It's the only obstacle to a sufficiently sophisticated mathematician. Now the roots of a polynomial are symmetric algebraically, but not numerically, so Buridan's Ass is not an obstacle for solving polynomials numerically (although it still shouldn't be ignored; after all, Newton's Algorithm starting from a real number never find a complex solution). The only thing that's left is the "trivial" portion of the problem.