Its the same because the uniform distribution over (-x,x) can be obtained by taking a random variable uniformly distributed over (-1,1) and multiplying it by x.

Its the same because the uniform distribution over (-x,x) can be obtained by taking a random variable uniformly distributed over (-1,1) and multiplying it by x. This doesn't change anything for the question about roots because the roots of a polynomial don't change when you multiply it by x.