| 1. | Thus, the real roots of a polynomial can be demonstrated graphically.
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| 2. | Thus, one can use factorization to find the roots of a polynomial.
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| 3. | Since all algebraic numbers ( including complex numbers ) are roots of a polynomial.
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| 4. | For a field containing all the roots of a polynomial, see the splitting field.
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| 5. | This definition generalizes the multiplicity of a root of a polynomial in the following way.
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| 6. | However, the problem of finding the roots of a polynomial can be very ill-conditioned.
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| 7. | The relation between the roots of a polynomial and its coefficients is described by Vieta's formulas.
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| 8. | It is possible to determine the bounds of the roots of a polynomial using Samuelson's inequality.
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| 9. | A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
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| 10. | Sometimes one or more roots of a polynomial are known, perhaps having been found using the rational root theorem.
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