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Answered

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

Verified Answer :

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

\(f(x)=3x^{6}+30x^{5}+75x^{4}\)    

Find the zeroes of the function

\(f(x)=3x^{6}+30x^{5}+75x^{4}\)  

\(f(x)=3x^{4}(x^{2}+10x+25)\)

 \(f(x)=3x^{4}(x+5)^{2}\)  

The zeroes of the function are

\(x=-5\) -------> with multiplicity \(2\)

\(x=0\) -------> with multiplicity \(4\)

therefore      

the answer is the option

–5 with multiplicity 2 and 0 with multiplicity 4    

see the attached figure

View image calculista

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