above the row containing the zeroes is called the "auxiliary polynomial". We have the following table: In such a case the auxiliary polynomial is which is again equal to zero. The next step is to differentiate the above equation which yields the polynomial . The coefficients of the row containing zero now become "8" and "24". The process of Routh array is proceeded using these values which yield two points on the imaginary axis. These two points on the imaginary axis are the prime cause of marginal stability. See also Control engineering Derivation of the Routh array Nyquist stability criterion Routh–Hurwitz theorem Root locus Transfer function Liénard–Chipart criterion (variant requiring fewer computations) Kharitonov's theorem (variant for unknown coefficients bounded within intervals) Jury stability criterion (analog for discrete-time LTI systems) Bistritz stability criterion (analog for discrete-time LTI systems) References Felix Gantmacher (J.L. Brenner translator) (1959). Applications of the Theory of Matrices, pp 177–80, New York: Interscience. Stephen Barnett (1983). Polynomials and Linear Control Systems, New York: Marcel Dekker, Inc. External links A MATLAB script implementing the Routh-Hurwitz test Online implementation of the Routh-Hurwitz Criterion Stability theory Electronic feedback Electronic amplifiers Signal processing Polynomials