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More generally, the distribution of the roots of a polynomial <math>p</math> with respect to an arbitrary circle in the complex plane, say one with centre <math>c</math> and radius <math>\rho</math>, can be found by application of the Schur-Cohn test to the 'shifted and scaled' polynomial <math>q</math> defined by <math>q(z)=p(c+\rho\,z)</math>.
Not every scaling factor is allowed, however, for the Schur-Cohn test can be applied to the polynomial <math>q</math> only if none of the following equalities occur: <math>T^{k}q(0)=0</math> for some <math>k=1,\ldots K</math> or <math>T^{K+1}q=0</math> while <math>d_K>0</math>. Now, the coefficients of the polynomials <math>T^{k}q</math> are polynomials in <math>\rho</math> and the said equalities result in polynomial equations for <math>\rho</math>, which therefore hold for only finitely many values of <math>\rho</math>. So a suitable scaling factor can always be found, even arbitrarily close to <math>1</math>.
===Lehmer's method===
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