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Citation bot (talk | contribs) Add: s2cid. | Use this bot. Report bugs. | Suggested by Smasongarrison | Linked from User:Smasongarrison/Sandbox | #UCB_webform_linked 131/3850 |
→Derivation of the method via Newton's method: Inserted a link to the Vieta's system |
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Those coefficients are, up to a sign, the [[elementary symmetric polynomial]]s <math>\alpha_1(\vec z),\dots,\alpha_n(\vec z)</math> of degrees ''1,...,n''.
To find all the roots of a given polynomial <math>f(X)=X^n+c_{n-1}X^{n-1}+\cdots+c_0</math> with coefficient vector <math>(c_{n-1},\dots,c_0)</math> simultaneously is now the same as to find a solution vector to the [[Vieta's_formulas|Vieta's system]]
:<math>\begin{matrix}
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