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I have a math problem in front of me, and after struggling three days with it, I cannot find the solution. I need to find the roots of this polynomial equation: $x^3+x^2+1=0$.

Anyone have a solution to this?

Any help is appreciated..

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    See http://www.wolframalpha.com/input/?i=solve+x%5E3+%2B+x%5E2+%2B+1+%3D+02012-09-10
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    http://www.proofwiki.org/wiki/Cardano%27s_Formula2012-09-10
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    @SeanEberhard I did that, however I am interested in the steps to the solution.2012-09-10
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    I would use Tartaglia-Cardano method, what is a lot of work.2012-09-10
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    @labbhattacharjee Thank you very much. Will check it out now.2012-09-10
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    You could proceed as follows: set $y=\frac 1 x$ so that $y^3+y+1=0$. Then set $y=u+v$ with $uv=-\frac 1 3$ which enables you to obtain expressions for $u^3+v^3$ and $u^3v^3$. Then you can solve a quadratic to get $u^3$ and $v^3$, which gives you $u$ and $v$ and hence $y$ and $x$.2012-09-10

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