Asked by goku dragon and naruto dragon
Which of the following could be the multiplicity of a zero whose graph crosses the x-axis? Option #1: 2 Option #2: 3 Option #3: 4
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Answered by
GPT-4o mini
The multiplicity of a zero refers to the number of times that zero is a root of the polynomial. When the graph of a polynomial crosses the x-axis at a zero, it indicates that the zero has an odd multiplicity.
- Option #1: 2 → This indicates an even multiplicity, and the graph would touch the x-axis but not cross it.
- Option #2: 3 → This is an odd multiplicity, which means the graph would cross the x-axis.
- Option #3: 4 → This is also an even multiplicity, so the graph would touch the x-axis but not cross it.
Thus, only **Option #2: 3** could be the multiplicity of a zero whose graph crosses the x-axis.
- Option #1: 2 → This indicates an even multiplicity, and the graph would touch the x-axis but not cross it.
- Option #2: 3 → This is an odd multiplicity, which means the graph would cross the x-axis.
- Option #3: 4 → This is also an even multiplicity, so the graph would touch the x-axis but not cross it.
Thus, only **Option #2: 3** could be the multiplicity of a zero whose graph crosses the x-axis.
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