Question

Multiplicity example

Answer 1

the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.

Explanation:

Answer 2

Mathwords: Multiplicity. 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.

Extra:

How do you find the multiplicity?

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The factor is repeated, that is, (x−2)2=(x−2)(x−2), so the solution, x=2, appears twice. The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor, x=2, has multiplicity 2 because the factor (x−2) occurs twice.

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