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38 votes
38 votes
40 Points!!!!!!!!!!

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) = 3(x + 7)(x + 3)^2?
A? B? C? D?

40 Points!!!!!!!!!! For the polynomial, list each real zero and its multiplicity. Determine-example-1
User Magnus Runesson
by
3.1k points

1 Answer

26 votes
26 votes

Answer:

B

Explanation:

You find the multiplicity by looking at the power of the original root. You can imagine it as
image. Now set those equal to 0 to find the value of them as roots.


image

Solve them both and you get:


image

Now as we saw in the origin of the roots above that (x + 7) was raised to the first power. That means it has a multiplicity of one, which also means it crosses when it reaches the x-axis. (x + 3) however had a multiplicity of 2, since it was squared. That means that (x + 3) will touch and turn the x-axis.

Therefore the answer is B since that agrees with everything we said.

User Oleg  Ignatov
by
2.7k points