Let f(x) = 0 be an equation involving the variable x. A root of the equation is a value h such that f(h) = 0. Such a value is also called a zero of the function f.
For a suitably differentiable function f, then h is said to be a root of order (or multiplicity) n if
If f(x) is a polynomial, this is equivalent to (x − h)n dividing f(x) but no greater power. A root of order greater than 1 is called a multiple root or repeated root.
See also order of contact, Vie`te’s formulae.