I woke up today doing me a question:
is there a complex number that is root of two different irreducible polynomials of $\mathbb{Q} [x]$?
I think not but I'm not sure and I am trying to prove. Some help?
2026-04-12 15:59:00.1776009540
A number root of two irreducible polynomials?
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Hint $\ f_1(r) = 0 = f_2(r)\,\Rightarrow \gcd(f_1,f_2)(r) = 0\,$ by $\,\gcd(f_1,f_2) = h_1 f_1\! + h_2 f_2\,$ by Bezout.