Help finding multiplicity and zeros?

MHB
Thread starter pita0001
Start date Mar 19, 2014
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multiplicity

In summary, multiplicity in mathematics refers to the number of times a given number or root appears as a solution to a polynomial equation. It is also known as the degree of a root. The multiplicity of a zero can be found by looking at the degree of the polynomial equation or the exponent on the corresponding factor if the equation can be factored. A zero can have a multiplicity of 0, meaning it is not a solution to the equation. The number of zeros a polynomial equation has is equal to its degree, counting multiplicities. A simple zero appears as a solution only once, while a zero with multiplicity greater than 1 appears multiple times.

Mar 19, 2014

pita0001

(x+4) (x-2)^3 (x^2+2x-8)

would it be -4 multiplicity of 2
and 2 multiplicity of 4?

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Mar 19, 2014

MarkFL

Gold Member

MHB

Yes, that's correct since the quadratic factor is the product of the other two linear factors.

Mar 27, 2014

HallsofIvy

Science Advisor

Homework Helper

in other words,
[tex](x+ 4)(x- 2)^3(x^2- 2x- 8)= (x+ 4)(x- 2)^3(x- 2)(x+ 4)= (x+ 4)^2(x- 2)^4[/tex]
as I am sure you realized.

Related to Help finding multiplicity and zeros?

1. What is multiplicity in mathematics?

In mathematics, multiplicity refers to the number of times a given number or root appears as a solution to a polynomial equation. It is also known as the degree of a root.

2. How do you find the multiplicity of a zero?

The multiplicity of a zero can be found by looking at the degree of the polynomial equation. If the degree is n, then the zero has a multiplicity of n. Additionally, if the equation can be factored, the multiplicity of a zero can be determined by the exponent on the corresponding factor.

3. Can a zero have a multiplicity of 0?

Yes, a zero can have a multiplicity of 0. This means that the zero is not a solution to the polynomial equation.

4. How do you determine the number of zeros a polynomial equation has?

The number of zeros a polynomial equation has is equal to its degree. This means that a polynomial equation of degree n will have n zeros, counting multiplicities.

5. What is the difference between a simple zero and a zero with multiplicity?

A simple zero has a multiplicity of 1, meaning it appears as a solution to the polynomial equation only once. A zero with multiplicity greater than 1 will appear as a solution to the equation multiple times, depending on the multiplicity value.