Definition:Multiple Root

Definition

A multiple root is a root of an equation which appears more than once.

Multiplicity

The multiplicity of a multiple root is the number of times it appears.

Examples

Arbitrary Example

Consider the cubic equation $\EE$:

$\EE: \quad x^3 - 3 x^2 + 4 = 0$

$\EE$ has two solutions: $-1$ and $2$.

$2$ is a multiple root of $\EE$ with multiplicity $2$.

Also known as

A multiple root of multiplicity $n$ is known as an $n$-tuple root.

It is also known as a repeated root.

Also see

• Definition:Double Root

• Results about multiple roots can be found here.

Sources

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