Table of Contents

## How do you find multiple zeros and multiplicity?

How To: Given a graph of a polynomial function of degree n , identify the zeros and their multiplicities.

- If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.
- If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity.

## What is the multiplicity of multiple zeros?

The polynomial p(x)=(x-1)(x-3)² is a 3rd degree polynomial, but it has only 2 distinct zeros. This is because the zero x=3, which is related to the factor (x-3)², repeats twice. This is called multiplicity. It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1.

**How do you write a zero with a multiplicity of 2?**

We have two unique zeros: −2 and 4 . However, −2 has a multiplicity of 2 , which means that the factor that correlates to a zero of −2 is represented in the polynomial twice. The zero at x=−2 “bounces off” the x -axis. This behavior occurs when a zero’s multiplicity is even.

**What is the multiplicity of 5?**

EXAMPLE

zero | multiplicity |
---|---|

53 | 7 |

0 | 4 |

8 | 3 |

### What does multiplicity mean in math?

number of values

The word multiplicity is a general term meaning “the number of values for which a given condition holds.” For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point.

### What are the zeros of the function what are their multiplicities?

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero. If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity. The sum of the multiplicities is n.

**What is a multiplicity of 4?**

How many times a particular number is a zero for a given polynomial. For example, in the polynomial function f(x) = (x – 3)4(x – 5)(x – 8)2, the zero 3 has multiplicity 4, 5 has multiplicity 1, and 8 has multiplicity 2.