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