Question

Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?

Answer 1

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

Answer 2

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.