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how to get exact solutions (error free solution)

Posted 10 years ago

I have a small problem.

sk = List[](*Here an empty list 'sk' is generated*)



PTT = x^900 + 4 x^100 - 
  5(*Here I have defined a polynomial "PTT" in x having degree 900*)

sk = x /. NSolve[PTT == 0, x];
(*     Here "PTT" is solved for 900 roots.
And all the soltuins of polynomial "PTT" are stored in the list sk   *)


For[i = 1, i < 11, i = i + 1,
 x = sk[[i]];
 Print[{x, PTT}]
 ]

(*This loop Substitute the first 10 solutions from the array "sk" in the \
polynomial "PTT"*)

{-1.00218-0.0203695 I,-3.78364*10^-13+2.10498*10^-13 I}

{-1.00218+0.0203695 I,-3.78364*10^-13-2.10498*10^-13 I}

{-1.00218-0.0277838 I,-2.82441*10^-13+1.42109*10^-13 I}

{-1.00218+0.0277838 I,-2.82441*10^-13-1.42109*10^-13 I}

{-1.00194-0.0351982 I,-3.73035*10^-13-7.32747*10^-14 I}

{-1.00194+0.0351982 I,-3.73035*10^-13+7.32747*10^-14 I}

{-1.0019-0.0129806 I,-2.75779*10^-13+2.85105*10^-13 I}

{-1.0019+0.0129806 I,-2.75779*10^-13-2.85105*10^-13 I}

{-1.00148-0.0425983 I,2.35367*10^-13+1.20792*10^-13 I}

{-1.00148+0.0425983 I,2.35367*10^-13-1.20792*10^-13 I}

When solutions of the polynomial are substutituted in equation, they must completly satisfy the polynomial.

But As Observed in the output, it is not so.

How can this error be removed.
I need exact solutions, which can satisfy the orignal equation

Mathematica code of this file can be found in attachments.

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