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## Main Question or Discussion Point

Is there a method to finding the roots of quartics besides Ferrari's formula?

I have the equation

[tex]x^{4}+5x^{2}+4x+5=0[/tex]

I know one of the factor is something like $$x^{2}+x+1$$ and the other one can be found using sythetic division, but how can I find the factors without knowing one of them in the first place?

Thanks.

My bad about the title. It's supposed to be Quartics instead of uartics.

I have the equation

[tex]x^{4}+5x^{2}+4x+5=0[/tex]

I know one of the factor is something like $$x^{2}+x+1$$ and the other one can be found using sythetic division, but how can I find the factors without knowing one of them in the first place?

Thanks.

My bad about the title. It's supposed to be Quartics instead of uartics.