Abstract: Consider the stability-robustness of a polynomial-family (assuming that the coefficients are affine functions of the parameters). This problem can be converted to an one-parameter simple quadratic programming (rank 2) by the zero-excluding principle. Using the theory of simple quadratic programming, the Khun-Tucker conditions and the method of perturbation analysis we derive a polynomial-time algorithm and solve the problem of computing complexity. Most of the availabe results in the literature, such as the Edge Theorem and the Extended Kharitonov's Theorem are special cases of the algorithm developed in this paper.