Is there any condtions in terms of coefficients, which is equivalent to two polynomials p and q having a common root inside the unit disc. More precisely, suppose that p and q are two complex polynomials. they have a common root inside the unit disc if and only if.....?
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5$\begingroup$ ...if and only if it is not true that $\gcd(p,q)$ has all roots outside the unit disc, reducing the problem to your previous question: mathoverflow.net/questions/67049/… . $\endgroup$– Emil JeřábekCommented Jun 20, 2011 at 13:41
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Deals with the question of one polynomial having a root outside the disk. For the current question, apply the algorithms described in the answers to the greatest common divisor of $p$ and $q$.
answered Jun 20, 2011 at 13:42