Question: Common root of certain polynomials

Nonzero complex numbers a, b, and c are such that every pair of the polynomials ( in x )
a*x^11+b*x^4+c, b*x^11+c*x^4+a, c*x^11+a*x^4+b has a common root. How to prove or disprove with Maple that all the three polynomials have a common root? I am aware of the resultant command in Maple.

Please Wait...