Michael Stifel (1487?-1567) condenses the previous eight formulas for the roots of a quadratic into one.

Francois Viete (1540-1603) solves the casus irreducibilis of the cubic using trigonometric functions.

Viete solves a particular 45th degree polynomial equation by decomposing it into cubics and a quintic. Later he gives a solution of the general cubic that needs the extraction of only a single cube root.

Albert Girard (1595-1632) conjectures that the nth degree equation has n roots counting multiplicity.

Rene Descartes (1596-1650) gives his rule of signs to determine the number of positive roots of a given polynomial.

Isaac Newton (1642-1727) finds a recursive way of expressing the sum of the roots to a given power in terms of the coefficients.

Newton introduces his iterative method for the numerical approximation of roots.

Newton invents Newton's parallelogram to approximate all the possible values of y in terms of x, if: