For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.

f(x)=4(x-7)(x-5)^4

Don't need to do the whole problem, just teach me how to do it if you can.

Question

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept.

f(x)=4(x-7)(x-5)^4

Don't need to do the whole problem, just teach me how to do it if you can.

anonymous · Answer

Ok figured out the zeros are 7, and 5 with a multiplicity of 4.

How do i tell if it touches or crosses the x-axis?

campbell_st · Answer

well do you know about the curve y = (x -1)^2   it has a root at 1... does it cut or touch the x-axis.?

anonymous · Answer

On my ti-89 it just touches the x-axis

campbell_st · Answer

so (x - 5)^4 does a similar thing... at x = 5

campbell_st · Answer

and what about x = 7... cuts or touches...

anonymous · Answer

So its always going to be right on my graphing calc?

campbell_st · Answer

here is my interpretation of the graph. 

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