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  "body": "\n## Definition\n\nLet $R$ be a [[ring|0894J980RK]] and let $f \\in R[x]$.\nAn element $c \\in R$ is a root of $f$ if $f(c) = 0$, where $f(c)$ is the [[value of $f$ at $c$|0GJ7T0NK49]].\n\n## Remarks\n\nThe roots of $x^2 - 1$ in $\\mathbb{Z}$ are $1$ and $-1$.\nThe polynomial $x^2 + 1$ has no root in $\\mathbb{R}$. It has the roots $i$ and $-i$ in $\\mathbb{C}$.\nBy the [[factor theorem|0K3MWA7DMC]], over a commutative ring, $c$ is a root of $f$ if and only if $x - c$ divides $f$.\n\n## Explanations\n\n### L1 human\n\nA root is a solution of the equation $f(x) = 0$.\nWhether a polynomial has a root depends on the ring: $x^2 - 2$ has no root in $\\mathbb{Q}$, but it has the root $\\sqrt{2}$ in $\\mathbb{R}$.\n",
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