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Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?
–5 with multiplicity 2 and 1/3 with multiplicity 4
5 with multiplicity 2 and 1/3 with multiplicity 4
–5 with multiplicity 2 and 0 with multiplicity 4
5 with multiplicity 2 and 0 with multiplicity 4

Respuesta :

Hagrid
The right answer for the question that is being asked and shown above is that: "–5 with multiplicity 2 and 0 with multiplicity 4" This is the statement that describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4.
calculista

we have

[tex]f(x)=3x^{6}+30x^{5}+75x^{4}[/tex]    

Find the zeroes of the function

[tex]f(x)=3x^{6}+30x^{5}+75x^{4}[/tex]  

[tex]f(x)=3x^{4}(x^{2}+10x+25)[/tex]

 [tex]f(x)=3x^{4}(x+5)^{2}[/tex]  

The zeroes of the function are

[tex]x=-5[/tex] -------> with multiplicity [tex]2[/tex]

[tex]x=0[/tex] -------> with multiplicity [tex]4[/tex]

therefore      

the answer is the option

–5 with multiplicity 2 and 0 with multiplicity 4    

see the attached figure

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