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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- Jul 20th 2009, 11:47 AMjanedoesolving 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 - Jul 20th 2009, 12:10 PMRandom Variable
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)?

- Jul 20th 2009, 12:12 PMCalculus26
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