College Algebra

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Multiplicity

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College Algebra

Definition

Multiplicity of a root in a polynomial function is the number of times that root occurs. It affects the shape and behavior of the graph at the corresponding $x$-intercept.

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5 Must Know Facts For Your Next Test

  1. The multiplicity of a root determines whether the graph touches or crosses the x-axis at that root.
  2. A root with an odd multiplicity will cause the graph to cross the x-axis.
  3. A root with an even multiplicity will cause the graph to touch but not cross the x-axis.
  4. The sum of all multiplicities in a polynomial equals its degree.
  5. Multiplicity influences local maxima, minima, and points of inflection near roots.

Review Questions

  • What is the effect on a polynomial's graph if a root has an odd multiplicity?
  • How does the graph behave at a root with even multiplicity?
  • If a polynomial has roots 2 (multiplicity 3) and -1 (multiplicity 1), what is its degree?
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