Are you sure??
I got a quadratic like r^2 - 11r + 1 = 0. In the two solutions that follow,one of them is negative. We keep the positive solution but discard the negative because......
We claim this is not possible because if r < 0 then x < 0 (xr = 4, remember?)
So xr^2 < 0. Contradiction because length of an edge cannot be negative!