let p be a non constant polynomial with degree n such that: p(z)=a_n z^n +...+a_0 show that if z∈C with∣z∣≥max{1,(2/(∣a_n ∣))Σ_(i=1) ^(n−1) ∣a_i ∣} then (1/2)∣a_n ∣∣z∣^n ≤∣p(z)∣≤(3/2)∣a_n ∣∣z∣^n (i already did the right side of the inequality so try to show ∣p(z)∣≥(1/2)∣a


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Question Number 171145 by floor(10²Eta[1]) last updated on 08/Jun/22
$let p be a non constant polynomial with degree n such that: p(z)=a_n z^n +...+a_0 show that if z∈C with∣z∣≥max{1,(2/(∣a_n ∣))Σ_(i=1) ^(n−1) ∣a_i ∣} then (1/2)∣a_n ∣∣z∣^n ≤∣p(z)∣≤(3/2)∣a_n ∣∣z∣^n (i already did the right side of the inequality so try to show ∣p(z)∣≥(1/2)∣a_n ∣∣z∣^n )$
$let p be a non constant polynomial with$ $degree n such that : p (z) = a_{n} z^{n} + . . . + a_{0}$ $show that if z \in C with ∣ z ∣⩾ \max {1, \frac{2}{∣ a_{n} ∣} \underset{i = 1}{\sum^{n - 1}} ∣ a_{i} ∣}$ $then \frac{1}{2} ∣ a_{n} ∣∣ z ∣^{n} ⩽∣ p (z) ∣⩽ \frac{3}{2} ∣ a_{n} ∣∣ z ∣^{n}$ $(i already did the right side of the inequality$ $so try to show ∣ p (z) ∣⩾ \frac{1}{2} ∣ a_{n} ∣∣ z ∣^{n})$
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