Question

What happens if the root has an even multiplicity?

A) The root is -2
B) The root is 1
C) The root is repeated twice
D) The root has no real solutions

Answer 1

If the root has an even multiplicity, the graph of the equation will bounce off the x-axis at the root, creating a local minimum or maximum point.

Step-by-step explanation:

If the root has an even multiplicity, it means that the root appears as a solution to the equation multiple times. A root with an even multiplicity will touch or intersect the x-axis and then turn back around, without crossing it. This means that the graph of the equation will bounce off the x-axis at the root, creating a local minimum or maximum point.

For example, if the root is -2, the equation might be (x + 2)^2 = 0, which means that x = -2 is a repeated root with an even multiplicity of 2. The graph of this equation would touch the x-axis at x = -2 and bounce back up, creating a local minimum point.