Let $n\in\mathbb N^\*$, $P(x)=a\_0+\dotsb+a\_{n-1}x^{n-1}+x^n$ and $r\_1,\dotsc,r\_n\in\mathbb C$ the roots of $P$.



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> Is it true $\lim\limits\_{\max(\lvert a\_i\rvert,i=0\dotsc n-1)\rightarrow 0} \max(\lvert r\_i\rvert,i=1\dotsc n)=0$?
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> If there is an inequality between the two maxes, can you give it?
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About roots of polynomials
See [an application](https://en.wikipedia.org/wiki/Geometrical_properties_of_polynomial_roots#From_Rouch%C3%A9_theorem) of Rouché's theorem to polynomials. As I remember, it is used in one of the proofs of The Fundamental Theorem of Algebra.


