He also showed that the roots of a cubic equation can be derived by means of the infinitesimal calculus.

Each of those is a root of a quadratic equation in terms of the one before.

After the elimination is done, one has to find the real roots of a single variable equation numerically.

He also obtained some evaluations of the number of real roots of an equation.

Originally Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other.

Any complex number which is a root of an equation where are integers will, said Dedekind, be called an algebraic number.

Stone gives an example of this: when computing the roots of a quadratic equation the computor must know how to take a square root.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

He used what would later be known as the "Ruffini-Horner method" to numerically approximate the root of a cubic equation.

This section describes how the roots of such an equation may be computed.