Sextic equation

Since a sextic function is defined by a polynomial with even degree, it has the same infinite limit when the argument goes to positive or negative infinity.

Some sixth degree equations, such as ax6 + dx3 + g = 0, can be solved by factorizing into radicals, but other sextics cannot.

There are formulas to test either case, and, if the equation is solvable, compute the roots in term of radicals.

[1] Watt's curve, which arose in the context of early work on the steam engine, is a sextic in two variables.

The describer "sextic" comes from the Latin stem for 6 or 6th ("sex-t-"), and the Greek suffix meaning "pertaining to" ("-ic").

Graph of a sextic function, with 6 real roots (crossings of the x axis) and 5 critical points . Depending on the number and vertical locations of minima and maxima , the sextic could have 6, 4, 2, or no real roots. The number of complex roots equals 6 minus the number of real roots.