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k=0 VI.1S.2. (Bonus) Prove the Joyal, Labelle, Rahman generalization of the Eneström-Kakeya The- orem: If p(z) = Σoak is
Posted: Wed May 04, 2022 10:26 am
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k=0 VI.1S.2. (Bonus) Prove the Joyal, Labelle, Rahman generalization of the Eneström-Kakeya The- orem: If p(z) = Σoak is a polynomial of degree n with real coefficients satisfying ao ≤ α₁ ≤ ... ≤ αn, then all the zeros of p lie in |z| ≤ (an-ao+|ao|)/|an|. HINT: Consider the function (12)p(z) = f(z) — anz¹+1 and mimic the proof of the Eneström-Kakeya Theorem.