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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 whether the graph crosses or touches the xaxis at each x intercept fx 3x 7x 32 A class=

Respuesta :

bradencarter

Answer:

B

Step-by-step explanation:

You find the multiplicity by looking at the power of the original root. You can imagine it as [tex](x+7)^1(x+3)^2[/tex]. Now set those equal to 0 to find the value of them as roots.

[tex]x+7=0\\x+3=0[/tex]

Solve them both and you get:

[tex]x=-7\\x=-3[/tex]

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.

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