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The multiplicity of a zero is important because it tells us how the graph of the polynomial will behave around the zero. For example, notice that the graph of f ( x) = ( x − 1) ( x − 4) 2 behaves differently around the zero 1 than around the zero 4 , which is a double zero.
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. Although this polynomial has only three zeros, we say that it has seven zeros counting multiplicity.
In mathematics, 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.
Multiplicity is just the degree (exponent) of each factor, or the amount of times a factor appears. If the multiplicity is even, the graph will “bounce” off the x-axis where that factor is zero.
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 x = 2, has multiplicity 2 because the factor (x−2) ( x − 2) occurs twice.
Zeros of polynomials (multiplicity) Given the graph of a polynomial and looking at its x-intercepts, we can determine the factors the polynomial must have. Additionally, we can determine whether those factors are raised to an odd power or to an even power (this is called the multiplicity of the factors).
Demonstrates how to recognize the multiplicity of a zero from the graph of its polynomial. Explains how graphs just "kiss" the x-axis where zeroes have even multiplicities.
