Question

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

Answer 1

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.

Answer 2

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