# Newton-Raphson Method - Third positive root

I don't quite understand what is the difference between approximating the first positive root of a function and third positive root of a function by using the Newton-Raphson formula. Can the following formula apply to finding the third positive root ?

$$x_{n+1}=x_n-\frac{f\:\left(x_n\right)\:}{f\:'\:\left(x_n\right)}$$

• Newton's method finds a root; which one depends on where you start. – Paul Sep 15 '16 at 9:26
• @Paul Thanks for help! do you mean it's depends the initial condition I picked up ? – phantom Sep 15 '16 at 9:28
• Yes - see answer below. – Paul Sep 15 '16 at 9:29

If $x_1$ is close to one of the roots, then the iteration will generally converge towards that root.