Question

Which of the following could be the multiplicity of a zero whose graph touches the x-axis then turns back?(1 point)

3

0

1

2

Answer 1

[AI-generated answer — Bot GPT 3.5]

2

Answer 2

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

The multiplicity of a zero refers to the number of times a corresponding factor appears in the factorization of a polynomial. If a zero touches the x-axis and then turns back, it means that the graph "bounces" off the x-axis at that point. In other words, the graph does not cross the x-axis at that zero.

For a zero to touch the x-axis and then turn back, it must have an even multiplicity. This is because an odd multiplicity would cause the graph to cross the x-axis at that zero.

Therefore, the possible multiplicities for a zero whose graph touches the x-axis then turns back are:

0 (No factor corresponding to that zero in the polynomial)
2 (Two identical factors corresponding to that zero in the polynomial)

So, the correct answer is:

0

2