True or false:

Let f, g, and h$\displaystyle \in\mathbb{C}[x]$be non-constant, relatively prime polynomials such that f + g = h. Then

$\displaystyle \max (\deg f, \deg g, \deg h) \leq n_0(fgh) - 1, $

where$\displaystyle n_0(f)$denotes the number of distinct roots of f.