well, could any one tell me how to prove this in the relation with newton raphson method? if $y$ is a root of $f(x)=0$ with multiplicity $p$,then iterative formula becomes $x_{n+1}=x_n-p[f(x_n)/f'(x_n)]$
we know in general for simple root the iteration formula is $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$