# When does Root have a third argument

In Mathematica "11.0.1 for Microsoft Windows (64-bit) (September 20, 2016)",

Root[#^4 + 1 &, 2];


actually has three arguments, as can be seen from

% // InputForm
(* Root[1 + #1^4 & , 2, 0] *)


This is well explained in 34764. However,

((zj /. (sol[[1]] // N))[[1, 1, 1, 2, 2]]);


where sol is defined here, has only two arguments.

% // InputForm
(* Root[..., 2] *)


What criteria does Root use to determine the number of its arguments? Note that both instances of Root were generated by Solve.

• What if you use FullForm? – xzczd Dec 30 '16 at 17:39
• @xzczd The number of arguments does not change. – bbgodfrey Dec 30 '16 at 17:41
• Further Root[] related fun: if the associated polynomial equations are sufficiently complicated (e.g. Solve[{x^3 y - x y^3 + x^2 z^3 + y^5 == 1, x^5 - x^2 y^3 + y^2 z == 1, x y^2 + y z^3 + x^2 y^2 + z^2 == -1}, {x, y, z}, Reals]), Root[] takes a more elaborate form, having lists of polynomials as its first argument and a list of (apparent) indices as the second argument. – J. M. will be back soon Dec 30 '16 at 17:46