Difference between revisions of "Vieta's Formulas"

Latest revision as of 13:40, 5 November 2021

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-=== Background ===
+#REDIRECT[[Vieta's formulas]]
-Let <math>P(x)={a_n}x^n+{a_{n-1}}x^{n-1}+\cdots+{a_1}x+a_0</math>,
-where the coefficient of <math>x^{i}</math> is <math>{a}_i</math>. As a consequence of the [[Fundamental Theorem of Algebra]], we can also write
-<center><math>P(x)=a_n(x-r_1)(x-r_2)\cdots(x-r_n)</math>,</center>
-where <math>{r}_i</math> are the roots of <math>P(x)</math>.
-Let <math>{\sigma}_k</math> be the <math>{}{k}</math>th [[symmetric sum]].
-=== Statement ===
-<math>\sigma_k = (-1)^k\cdot \frac{a_{n-k}}{a_n{}}</math>, for <math>{}1\le k\le {n}</math>.
-=== Proof ===
-[needs to be added]