Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
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Let P"n(x)=x^m+p"m"-"1(n)x^m^-^1+...+p"1(n)x+p"m(n) be a parametrized family of polynomials of a given degree with complex coefficients p"k(n) depending on a parameter n@?Z"="0. We use Rouche's theorem to obtain approximations to the complex roots of P"n(x). As an example, we obtain approximations to the complex roots of the quintic polynomials P"n(x)=x^5+nx^4-(2n+1)x^3+(n+2)x^2-2x+1 studied by A. M. Schopp.