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-   MattcAnderson (https://www.mersenneforum.org/forumdisplay.php?f=146)

 MattcAnderson 2021-09-09 06:18

polynomial formula

Hi all,

Linear equations can be written as y=m*x+b.
This can be graphed as a straight line on an x y axis.

The general form of a quadratic (or second order polynomial) is
y = a*x^2+b*x+c
If we set this y = 0 and find roots, we have our standard quadratic formula.

x = (-b +/- sqrt(b^2 - 4*a*c))/(2*a)

For the cubic polynomial, see some nice work of Kevin Wortman at The University of Utah.
[URL="www.math.utah.edu/~wortman/1060text-tcf.pdf"]www.math.utah.edu/~wortman/1060text-tcf.pdf[/URL]

There is a 4th order polynomial formula using only addition, subtraction, multiplication, divistion, and nth roots of unity.

For general 5th order polynomials and higher, there is no formula using only addition, subtraction, multiplication, division, and roots of unity. Special functions are required.

Regards,
Matt

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