Obtain info about the differential equation of LegendreP with respect to x?

Questions
1

Hello, members of Mathematica community.

I would like to ask you about the method which Mathematica uses to find the roots of differential equation of LegendreP with respect to x.
dLegendreP/dx=0 .
Also how big of standard error ( or relative error) does this method give for the roots of dP/dx=0.

2

I expect that the method is the same as for other polynomial or analytic functions. If you start with exact data, the results are symbolic Root objects and can be computed with arbitrary precision.