Question

Odd multiplicities have which of the following effects on the x-axis?

Answer 1

The graph cuts the x-axis at odd multiplicities.

Explanation:

Let

`p(x) = {(x - a)}^(n)`

Then x-a has multiplicity n.

This determines whether, the x-intercept x=a cuts the x-axis or just touches it.

If n is even, the graph of p(x) just touches or becomes a tangent to the x-axis.

If n is odd , the graph cuts the x-axis.