Considering the case of cubic polynomials with integer coefficients and three real but irrational roots. Is it true that it's impossible that all three roots can be in the form of simple surd expressions like [tex]r+s \sqrt{n}[/tex] (where r and s are rational and sqrt(n) is a surd). The arguement is that if [tex]r+s \sqrt{n}[/tex] is a solution then you can show that [tex]r-s \sqrt{n}[/tex] must also be a solution.(adsbygoogle = window.adsbygoogle || []).push({});

Does anyone have any extra info or links to theorems or other useful info related to this.

Thanks.

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# Cubic with three real irrational roots.

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