Find all real zeros of the function f(×)=4(×+6)2(×2-36)(×-6)
1 answer:
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Answer:
the multiplicity is 4
Step-by-step explanation:
The graph shows a root at x = -2 that has a multiplicity of 2. You know the multiplicity is even, because the graph does not cross the x-axis. The multiplicity is 2 because the general shape of the graph in that area matches that of a quadratic (parabola).
The multiplicity of the root at x=4 is also an even number, because the x-axis is not crossed. However, the graph is significantly flatter at that point (than at x=-2), meaning the multiplicity is greater than 2. It is at least 4.
When we draw a graph with a multiplicity of 6 at x=4, we find the ratio of the peaks near x=-4 and x=0 to be different from that shown here. The suggests that the multiplicity of the root at x=4 is exactly 4.
