1
$\begingroup$

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 $K$.

$\endgroup$
  • 3
    $\begingroup$ The question is ambiguous in several ways, please revise and clarify. $\endgroup$ – MCH Jan 24 '13 at 3:57
  • 4
    $\begingroup$ At most $K$ or at least $K$? $\endgroup$ – arnab Jan 24 '13 at 8:32
3
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.