Zeros and multiplicities

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What is a zero of a polynomial function?

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A zero of a polynomial function is a value of x for which the function evaluates to zero. It represents the x-intercepts of the graph of the function.

Tags

CCSS.HSF-IF.C.7C

Front

Define multiplicity in the context of polynomial zeros.

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial function. A zero with multiplicity greater than 1 indicates that the graph touches or crosses the x-axis at that point.

Tags

CCSS.HSF-IF.C.7C

Front

How do you determine the multiplicity of a zero from a polynomial function?

Back

The multiplicity of a zero can be determined by examining the factors of the polynomial. If a factor is raised to a power, that power indicates the multiplicity of the corresponding zero.

Tags

CCSS.HSF-IF.C.7C

Front

Write a polynomial function with zeros at -1, 2, and 7, each with multiplicity 1.

Back

Tags

CCSS.HSF-IF.C.7C

Front

Back

The zeros are -2 with multiplicity 10 and 12 with multiplicity 9.

Tags

CCSS.HSF-IF.C.7C

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Back

The multiplicity is 2.

Tags

CCSS.HSF-IF.C.7C

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Back

The zeros are -4 with multiplicity 2, -8 with multiplicity 3, and 5 with multiplicity 1.

Tags

CCSS.HSF-IF.C.7C

Front

If a polynomial has a zero of multiplicity 3, how does this affect its graph?

Back

A zero of multiplicity 3 means the graph will touch the x-axis at that zero and turn around, creating a point of inflection.

Front

What does it mean if a zero has an even multiplicity?

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If a zero has an even multiplicity, the graph will touch the x-axis at that zero but will not cross it.

Front

What does it mean if a zero has an odd multiplicity?

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If a zero has an odd multiplicity, the graph will cross the x-axis at that zero.