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  "body": "\n## Summary\n\nA polynomial is solvable by radicals when all its roots can be written from its coefficients with the four field operations and $n$-th roots.\nFormally, its splitting field lies in a [[radical extension|V74WMGQQ9D]] of the base field.\nIn characteristic $0$, [[Galois' theorem|VHCWCFA3MX]] says this holds exactly when the [[Galois group of the polynomial|0JZY3R908H]] is [[solvable|0P3KZK0FTV]].\n\n## Explanations\n\n### L1 human\n\nThe quadratic formula shows that every equation $ax^2 + bx + c = 0$ is solvable by radicals: its roots are $(-b \\pm \\sqrt{b^2 - 4ac})/(2a)$.\nThe [[cubic formula|FB6J5WAT5V]] and the [[quartic formula|4CDFMKKZ01]] do the same for degrees $3$ and $4$.\nThe [[Abel–Ruffini theorem|163A2WQQJX]] says that no such formula exists for the general equation of degree $5$.\nSome quintics are still solvable by radicals, such as $x^5 - 2 = 0$, whose roots are $\\sqrt[5]{2}$ times the fifth roots of unity.\n",
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