# Hudde's rules

In mathematics, **Hudde's rules** are two properties of polynomial roots described by Johann Hudde.

1. If *r* is a double root of the polynomial equation

- and if are numbers in arithmetic progression, then
*r*is also a root of - This definition is a form of the modern theorem that if
*r*is a double root of*ƒ*(*x*) = 0, then*r*is a root of*ƒ*'(*x*) = 0.

2. If for *x* = *a* the polynomial

- takes on a relative maximum or minimum value, then
*a*is a root of the equation - This definition is a modification of Fermat's theorem in the form that if
*ƒ*(*a*) is a relative maximum or minimum value of a polynomial*ƒ*(*x*), then*ƒ*'(*a*) = 0.

## References

- Carl B. Boyer, A history of mathematics, 2nd edition, by John Wiley & Sons, Inc., page 373, 1991.

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