Does there exist a closed form expression for roots of polynomials of the form $$x^n + bx + c$$
Where $n \in \mathbb{N}$. $n$ need not be less than five.
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3the answer seems to be "No" https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem – Peter Melech Mar 22 '16 at 10:57
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7For $n=5$ and $b,c\in\Bbb Q$, the answer is "if and only if there exist $\mu,\nu\in\Bbb Q$ such that $b=\frac{5\mu^4(4\nu+3)}{\nu^2+1}$ and $c=\frac{4\mu^5(2\nu+1)(4\nu+3)}{\nu^2+1} $". – Mar 22 '16 at 10:57
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2You might also be interested in the Bring radical. Some quick facts here, here and here. – Mar 22 '16 at 11:07