For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh–Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over (Formula presented.). Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures.