Number of common roots and resultant of two tropical univariate   polynomials
  It is well known that for two univariate polynomials over complex number field the number of their common roots is equal to the order of their resultant. In this paper, we show that this fundamental relationship still holds for the tropical polynomials under suitable adaptation of the notion of order, if the roots are simple and non-zero. 
Hoon Hong, J. Rafael Sendra
math.AG