From Wikipedia on Marden's Theorem:

"A more general version of the theorem, due to Linfield (1920), applies to polynomials p(z) = (z − a)i (z − b)j (z − c)k whose degree i + j + k may be higher than three, but that have only three roots a, b, and c. For such polynomials, the roots of the derivative may be found at the multiple roots of the given polynomial (the roots whose exponent is greater than one) and at the foci of an ellipse whose points of tangency to the triangle divide its sides in the ratios i : j, j : k, and k : i."