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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>,
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| − | 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
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| − | <center><math>P(x)=a_n(x-r_1)(x-r_2)\cdots(x-r_n)</math>,</center>
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| − | where <math>{r}_i</math> are the roots of <math>P(x)</math>.
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| − | | |
| − | Let <math>{\sigma}_k</math> be the <math>{}{k}</math>th [[symmetric sum]].
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| − | | |
| − | === Statement ===
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| − | Vieta's says that <math>\sigma_k = (-1)^k\cdot \frac{a_{n-k}}{a_n{}}</math>, | |
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| − | for <math>{}1\le k\le {n}</math>.
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| − | | |
| − | === Proof ===
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| − | [needs to be added]
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