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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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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 $q$.

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