Definition:Root of Equation

Definition

Let $\map E x$ be a mathematical expression representing an equation which is dependent upon a variable $x$.

A root of $\map E x$ is a constant which, when substituted for $x$ in $\map E x$, makes $\map E x$ a true statement.

Extraction of Root

The process of finding roots of a given equation is referred to as extraction.

Examples

Arbitrary Quadratic

Consider the equation:

$\map E x := x^2 - x - 6 = 0$

The roots of $\map E x$ are:

\(\ds x\)

\(=\)

\(\ds -2\)

\(\ds x\)

\(=\)

\(\ds 3\)

Also see

• Results about roots of equations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): root: 1. (of an equation)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): root: 1. (of an equation)