Vieta's formulas explained

In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.^[1] They are named after François Viète (more commonly referred to by the Latinised form of his name, "Franciscus Vieta").

Basic formulas

Any general polynomial of degree n$$P(x)\; =\; a\_n\; x^n\; +\; a\_x^\; +\; \backslash cdots\; +\; a\_1\; x\; +\; a\_0$$(with the coefficients being real or complex numbers and) has (not necessarily distinct) complex roots by the fundamental theorem of algebra. Vieta's formulas relate the polynomial coefficients to signed sums of products of the roots as follows:

Notes and References

1. Web site: Weisstein . Eric W. . 2024-06-22 . Vieta's Formulas . MathWorld--A Wolfram Web Resource.