Resolvent

A resolvent in polynomial algebra is an auxiliary polynomial with coefficients in the same field as those of a given polynomial, whose roots are expressions in the roots of that polynomial. Resolvents are used to study or solve the original polynomial equation (Jensen et al. 2002, p. 23).

For a quartic equation with roots through , the three expressions

are the roots of its resolvent cubic.

In operator theory, the term resolvent also denotes the resolvent operator.