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 $\displaystyle{M=1+\sum_{k=0}^{n}|a_k|}$
Exercise of roots of a polynomial
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polynomials
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0Hi Jonas. I honestly thought the exercise but not to use: ( – 2012-12-07
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0Induction tried but did not succeed – 2012-12-07
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1As 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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0Excuse me Don Antonio. The exercise refers to the real roots of the polynomial – 2012-12-07
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0At first I did not know about that .. but lately if I accept all the answers to my questions. – 2012-12-07