Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

The multiplicity of a zero represents the number of times a factor is repeated in the factorization of the polynomial. If a graph crosses the x-axis at a certain zero, it means that the factor corresponding to that zero changes sign as it crosses the x-axis. In other words, the multiplicity must be an odd number.

Therefore, the multiplicity of a zero whose graph crosses the x-axis cannot be 2 (Option #1) or 4 (Option #3), since both of these are even numbers.

The only valid option is therefore Option #2: 3.

Answer 2

[AI-generated answer — Step-by-Step Bot]

The multiplicity of a zero refers to the number of times a zero appears as a root of the corresponding polynomial. In this case, if a graph crosses the x-axis at a certain point, it indicates that the corresponding zero has an odd multiplicity.

Therefore, Option #2: 3 is the correct choice, as an odd multiplicity represents a zero whose graph crosses the x-axis.