<p>You can (without too much work) find a number $K$ such that if $|x| &gt; K$ then $|a_n x^n| &gt; \sum_{k&lt;n} |a_k x^k|$, and so all roots are inside $(-K,K)$ and the distance between them is smaller than $2K$.</p>

CC BY-SA 3.0
2013-01-24T04:32:20.483Z
2013-01-24T04:32:20.483Z
Yuval Filmus
<p>Given a polynomial of degree $n$, namely, $y=a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$, with $a_i\in \mathbb{R}$,  I would to know if it is possible to <strong>compute</strong> a rational number $K$ such that the distance between each of the (at most $n$) real roots of the polynomial is $K$.</p>

CC BY-SA 3.0
2013-01-24T03:57:18.107Z
The question is ambiguous in several ways, please revise and clarify.
Mahdi Cheraghchi
CC BY-SA 3.0
2013-01-24T08:32:18.720Z
At most $K$ or at least $K$?
arnab
<na.numerical-analysis><computable-analysis>
Delimiting the roots of a polynomial
LORE81
# Delimiting the roots of a polynomial

(Asked by: username_0 on 2013-01-24)

Given a polynomial of degree $n$, namely, $y=a\_nx^n + a\_{n-1}x^{n-1} + \dots + a\_1x + a\_0$, with $a\_i\in \mathbb{R}$, I would to know if it is possible to **compute** a rational number $K$ such that the distance between each of the (at most $n$) real roots of the polynomial is $K$.

**Tags:** na.numerical-analysis, computable-analysis
> **Comments:**
> **username_1**: The question is ambiguous in several ways, please revise and clarify.  
> **username_2**: At most $K$ or at least $K$?  

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## 1 answers

### Answer by username_3 on 2013-01-24. Score: 3

You can (without too much work) find a number $K$ such that if $|x| > K$ then $|a\_n x^n| > \sum\_{k


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