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Math Help - solving this for x (zero of the function)

  1. #1
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    solving this for x (zero of the function)

    I can't seem to figure out how to solve this for x without graphing it:

    0=x^3-3x+1
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  2. #2
    Super Member Random Variable's Avatar
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    Sometimes with cubics you can find one zero just by inspection and then the other two by synthetic division. Not so in this case. Is this problem in a section about approximating roots (i.e, Newton's method)?
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  3. #3
    MHF Contributor Calculus26's Avatar
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    Ideally we would start with the rational roots theorem but here the only possible zeroes are -1 and 1 neither of which are zeroes.

    Graphically is the best way to go here. the cubic equation is rather long and involved but:

    If interested see Solving Cubic Equations


    I would agree it would be simpler to use Newton's Method
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