Vieta's Formulas for Polynomial Roots

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This Demonstration shows the relationships between the coefficients of a general polynomial of degree and its roots. These relationships are known as Vieta's formulas. They can be used for real and complex roots, but this Demonstration considers only small integer roots.


Consider the polynomial


Every coefficient can be obtained by


When , the polynomial is rewritten as

, with .

Similarly, when , the polynomial is rewritten as

, with .


Contributed by: D. Meliga, L. Lavagnino and S. Z. Lavagnino (February 2019)
Open content licensed under CC BY-NC-SA



[1] E. W. Weisstein. "Vieta's Formulas" from Wolfram MathWorld—A Wolfram Web Resource. (Wolfram MathWorld).


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