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How to prove that all the roots of the polynomial $f(x)=a_o+a_1 x+\cdots+ x^n$ with real coefficients belong to the interval $ [-M, M] $, with $\displaystyle{M=1+\sum_{k=0}^{n}|a_k|}$

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    Hi Jonas. I honestly thought the exercise but not to use: (2012-12-07
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    Induction tried but did not succeed2012-12-07
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    As written the claim is false, since the roots of $\,x^2+1\in\Bbb R[x]\,$ do *not* belong to the interval $\,[-3,3]\,$ ...Are there any other conditions on the polynomial?2012-12-07
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    Excuse me Don Antonio. The exercise refers to the real roots of the polynomial2012-12-07
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    At first I did not know about that .. but lately if I accept all the answers to my questions.2012-12-07

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