If $f ( x ) = \frac { x ^ { n } } { n ! } + \frac { x ^ { n - 1 } } { ( n - 1 ) ! } + \cdots + x + 1$, then show that $f ( x ) = 0$ has no repeated roots.
If $f ( x ) = \frac { x ^ { n } } { n ! } + \frac { x ^ { n - 1 } } { ( n - 1 ) ! } + \cdots + x + 1$, then show that $f ( x ) = 0$ has no repeated roots.