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ExactRootIsolation


I notice also that Root has an invisible third argument

Solve[x^7 + 4*x^3 + 2*x + 1 == 0];

lst = x /. %
{Root[1 + 2*#1 + 4*#1^3 + #1^7 & , 1], Root[1 + 2*#1 + 4*#1^3 + #1^7 &
, 2], Root[1 + 2*#1 + 4*#1^3 + #1^7 & , 3],
  Root[1 + 2*#1 + 4*#1^3 + #1^7 & , 4], Root[1 + 2*#1 + 4*#1^3 + #1^7 &
, 5], Root[1 + 2*#1 + 4*#1^3 + #1^7 & , 6],
  Root[1 + 2*#1 + 4*#1^3 + #1^7 & , 7]}

(#1[[1]] & ) /@ lst
{1 + 2*#1 + 4*#1^3 + #1^7 & , 1 + 2*#1 + 4*#1^3 + #1^7 & , 1 + 2*#1 +
4*#1^3 + #1^7 & , 1 + 2*#1 + 4*#1^3 + #1^7 & ,
  1 + 2*#1 + 4*#1^3 + #1^7 & , 1 + 2*#1 + 4*#1^3 + #1^7 & , 1 + 2*#1 +
4*#1^3 + #1^7 & }

(#1[[2]] & ) /@ lst
{1, 2, 3, 4, 5, 6, 7}

(#1[[3]] & ) /@ lst
{0, 0, 0, 0, 0, 0, 0}

What is this third agument? 

Thanks


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