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  "body": "\n## Summary\n\nThe resultant of two polynomials is a polynomial expression in their coefficients that, for nonzero leading coefficients, vanishes exactly when they have a common root.\nIt is the [[determinant|00KDZRW4C0]] of the Sylvester matrix built from the coefficients.\nIt lets one decide whether two polynomial equations have a common solution without solving them.\nThe [[discriminant|0VVK64Q4JK]] of $f$ is, up to a simple factor, the resultant of $f$ and its derivative.\n\n## Explanations\n\n### L1 human\n\nTwo polynomials either share a root or they do not.\nThe resultant is a single number, computed from the coefficients alone, that is zero in the first case and nonzero in the second.\nFor $x - a$ and $x - b$ the resultant is $a - b$, which is zero exactly when the two roots agree.\nThe [[definition|8D277VG29T]] gives the matrix.\n",
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