The roots are:
[tex]\bullet \ x=-2 \ with \ multiplicity \ of \ 2 \\ \\ \bullet \ x=4 \\ \\ \bullet \ x=-1 \ with \ multiplicity \ of \ 3[/tex]
Explanation:
We have the following polynomial function:
[tex]f(x) = (x+2)^2(x-4)(x+1)^3[/tex]
The roots of any polynomial functions are those x-values at which the function equals zero. So, in order to find the roots for this function, we set [tex]f(x)=0[/tex]. So:
[tex](x+2)^2(x-4)(x+1)^3=0 \\ \\ \\ So \ we \ have \ the \ product \ of \ some \ factors \ then: \\ \\ The \ roots \ are: \\ \\ \\ \bullet \ x=-2 \ with \ multiplicity \ of \ 2 \\ \\ \bullet \ x=4 \\ \\ \bullet \ x=-1 \ with \ multiplicity \ of \ 3[/tex]
Finally, the graph of this function is shown below and the roots are also indicated.
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Parabola: https://brainly.com/question/10525169
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