Geodesic
Zeros of Linear Combinations of Polynomials
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 139-142

Voir la notice de l'article provenant de la source Cambridge University Press

The following theorem is due to J. L. Walsh (see [2, Theorem 17, 2a]):Theorem. If all the zeros of f1(z)=zn+a1zn-1+ ... + an lie in or on the circle C1 with centre c1 and radius r1 and if all the zeros of f2(z)=zn+b1zn-1+ ... + bn lie in or on the circle C2 with centre c2 and radius r2, then each zero of the polynomial lies in at least one of the circles Γk with centre γk and radius ρk, where and where the ωk (k= 1, 2,..., n) are the nth roots of λ. 
Rahman, Q. I. Zeros of Linear Combinations of Polynomials. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 139-142. doi: 10.4153/CMB-1972-026-9
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[1] 1. Dieudonné, J., Sur quelques propriétés des polynômes. Actualités Sci. Indust. No. 114, Hermann, Paris, 1934. Google Scholar

[2] 2. Marden, M., Geometry of polynomials, Math. Surveys No. 3, Amer. Math. Soc, Providence, R.I., 1966. Google Scholar

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