Abel–Ruffini theorem

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What Wikipedia says

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipulated as indeterminates.

Excerpt from the Wikipedia article “Abel–Ruffini theorem”, under the CC BY-SA 4.0 license. Read the article on Wikipedia

Image: Johan Gørbitz, Public domain, via Wikimedia Commons.