XII.

Quadratic Equations.

An equation which contains the square of the unknown number, but no higher power, is called a quadratic equation.

A quadratic equation which involves but one unknown number as $x$, can contain only:

1. Terms involving the square of $x$.

2. Terms involving the first power of $x$.

3. Terms which do not involve $x$.

Collecting similar terms, every quadratic equation can be made to assume the form $a{x}^2+bx+c=0,$ where $a$, $b$, and $c$ are known numbers, and $x$ the unknown number.

If $a$, $b$, $c$ are numbers expressed by figures, the equation is a numerical quadratic. If $a$, $b$, $c$ are numbers represented wholly or in part by letters, the equation is a literal quadratic.

In the equation $a{x}^2+bx+c=0$, $a$, $b$, and $c$ are called the coefficients of the equation. The third term, $c$, is called the constant term.

If the first power of $x$ is wanting, the equation is a pure quadratic; in this case $b=0$.

If the first power of $x$ is present, the equation is an affected or complete quadratic.