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.....?



roots of polynomials
[This question](https://mathoverflow.net/questions/67049/roots-of-polynomials-outside-the-unit-disc)


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 $q$.


