let-p-x-x-n-a-n-1-x-n-1-a-1-x-a-o-if-is-roots-of-p-x-prove-that-1-max-0-i-n-1-a-i-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 31491 by abdo imad last updated on 09/Mar/18

let p(x)= x^n +a_(n−1) x^(n−1) +.... a_1 x +a_o if ξ is roots of p(x) prove that ∣ξ∣ ≤ 1+max_(0≤i≤n−1) ∣a_i ∣

$${let}\:{p}\left({x}\right)=\:{x}^{{n}} \:+{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} \:+….\:{a}_{\mathrm{1}} {x}\:+{a}_{{o}} \\ $$$${if}\:\:\xi\:\:{is}\:{roots}\:{of}\:{p}\left({x}\right)\:{prove}\:{that}\:\mid\xi\mid\:\leqslant\:\mathrm{1}+{max}_{\mathrm{0}\leqslant{i}\leqslant{n}−\mathrm{1}} \:\mid{a}_{{i}} \mid \\ $$

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