Large roots yield large coefficients. An addendum to: “The roots of a polynomial vary continuously as a function of the coefficients” [Proc. Amer. Math. Soc. 100 (1987), no. 2, 390–392; MR0884486 (88h:30006)]

Harris, Gary; Martin, Clyde

doi:10.1090/S0002-9939-1988-0934880-2

Large roots yield large coefficients. An addendum to: “The roots of a polynomial vary continuously as a function of the coefficients” [Proc. Amer. Math. Soc. 100 (1987), no. 2, 390–392; MR0884486 (88h:30006)]
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by Gary Harris and Clyde Martin

Proc. Amer. Math. Soc. 102 (1988), 993-994

DOI: https://doi.org/10.1090/S0002-9939-1988-0934880-2

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Original Article: Proc. Amer. Math. Soc. 100 (1987), 390-392.

Abstract:

We provide the details to the argument that the map $\hat \sigma$, defined in the above named paper, is open. We do this by including two trivial arguments that a polynomial with a big root must also have a big coefficient.

References

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Gary Harris and Clyde Martin, The roots of a polynomial vary continuously as a function of the coefficients, Proc. Amer. Math. Soc. 100 (1987), no. 2, 390–392. MR 884486, DOI 10.1090/S0002-9939-1987-0884486-8