Factor $a x^n + b x + c = 0$

Asked Jun 05 '22 at 19:22

Active Jun 05 '22 at 19:22

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I wish to factor the polynomial equation

$$a x^n + b x + c = 0$$

When $a = b$ and $n=5$, we have the Bring-Jerrard normal form of the quintic $x^5 + x + c = 0$. Using the Lagrange Inversion theorem, I could calculate a series solution for $x$, which is exactly the way that Bring radicals were developed. Is there any alternative formulation based solely on algebraic approaches, or is a convergent series easiest?

asked Jun 05 '22 at 19:22

Talmsmen

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This question is similar since it asks for the roots of a general trinomial, which help factor it – Тyma Gaidash Jun 05 '22 at 19:35
Do you want to factor this expression over $\mathbb Q$ or just calculate the roots ? In general, there won't be a solution by radicals. – Peter Jun 05 '22 at 20:33

Factor $a x^n + b x + c = 0$

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