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