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I want to solve my quintic equation with methods Newton and Bisection , and compare them. And I want to know, how to call Nsolve or Roots and told them that they use only for example Bisection algorithm.

PM: I dont want to write these algorithms myself

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  • $\begingroup$ "I want to know, how to call NSolve ... and tell them that they use only for example Bisection algorithm. I don't want to write these algorithms myself." - none of the built-ins use bisection, so you really will need to write it yourself. (OK, technically, the Brent algorithm used by FindRoot[] can take a bisection step, but it has a lot of other things going on.) OTOH, FindRoot[] can be made to use Newton's method, see this for example. $\endgroup$ – J. M.'s technical difficulties Apr 16 at 14:41
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    $\begingroup$ Search this site for "bisection method." One almost never has to write things themselves these days, if one is resourceful enough. $\endgroup$ – Michael E2 Apr 16 at 14:48
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For Newton

FindRoot[{x^5 - x + 1 == 0}, {x, 1}]

Then check the details with

Options@FindRoot

Check in the documentation the option Method in particular.

For the bisection method, NSolve may use it but it is a such a big machine that you will never know what it has done. NSolve gives all the roots. It knows it is a polynomial equation. It has special methods for this.

NSolve[{x^5 - x + 1 == 0}, x]

If you would like to experiment with bisection, doing it yourself would be easier and more instructive than trying to know what NSolve is doing.

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