Question

Which of the following could be the multiplicity of a zero whose graph touches the x-axis then turns back?
1
3
2
0

Answer 1

When the graph of a polynomial touches the x-axis and then turns back, it indicates that the zero at that point has an even multiplicity. This is because even multiplicities do not cross the x-axis but instead result in the graph intersecting tangentially.

Among the options provided:

- **1**: This is an odd multiplicity and would cross the x-axis.
- **3**: This is also an odd multiplicity and would cross the x-axis.
- **2**: This is an even multiplicity, which allows the graph to touch the x-axis and turn back.
- **0**: This concept does not apply to multiplicity in the context of zeros.

Thus, the only option from the list that could represent the multiplicity of a zero where the graph touches the x-axis and turns back is:

**2**.