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

1 answer

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.