Cubic Equations.

Cubic Equations. A cubic equation in a given quantity is an equation in which the highest exponent of that quantity in any term is 3. Every such equation can be reduced to the form $x^3\; +\; px\; +\; q\; =\; 0$, where $x$ is the variable and $p$ and $q$ are constants. Every equation of this form has three roots, all of which may be real, or one may be real and two imaginary. An equation containing any number of variables in which the greatest sum of the exponents of the variables in any term is 3 is called a cubic equation. Thus $x^2y\; +\; 5y^2\; +\; 6\; =\; 0$ and $xyz\; +\; z^2\; =\; 0$ are cubic equations in $x$, $y$, and $z$, respectively. See EQUATIONS.