Help finding multiplicity and zeros?

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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.
  • #1
pita0001
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(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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  • #2
Yes, that's correct since the quadratic factor is the product of the other two linear factors.
 
  • #3
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.
 

FAQ: Help finding multiplicity and zeros?

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.

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.

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.

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.

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.

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