what are the zeros of the function? what are their multiplicities? f(x)=3x^3+12x^2+9x a)the numbers-3,-1,and 0 are zeros of multiplicity 2 b)the numbers 3,1,0 are zero of multiplicity 1c)the numbers -3,-1,0 are zeros of multiplicity 1 d) the numbers 3,1,0 are zeros of multiplicity 2

Question

what are the zeros of the function? what are their multiplicities? f(x)=3x^3+12x^2+9x  a)the numbers-3,-1,and 0 are zeros of multiplicity 2 b)the numbers 3,1,0 are zero of multiplicity 1c)the numbers -3,-1,0 are zeros of multiplicity 1 d) the numbers 3,1,0 are zeros of multiplicity 2

anonymous · Answer

cats

anonymous · Answer

seems about right

anonymous · Answer

I like cats too I just used dogs as a username

mathmale · Answer

xxferrocixx and petewe:  stop dogging dogs.

mathmale · Answer

In regard to the zeros of f(x)=3x^3+12x^2+9x:  You have at least two possible approaches to choose from:  (1) find the zeros yourself (as by factoring and/or synthetic division), or (2) substitute each x value from the given sets of supposed zeroes into f(x)=3x^3+12x^2+9x to determine whether each is or is not a zero of f(x).

campbell_st · Answer

well if you have 3 zeros in a cubic they will all have multiplicity of 1. 

the degree of the leading term and the multiplicity are always equal

campbell_st · Answer

so you can test the zeros by using the factor theorem,

mathmale · Answer

Campbell:  That's an interesting assertion you've made about the degree of the leading term and the multiplicity being equal.  
My understanding is that "multiplicity" refers to how many times a given x value appears as a zero of the polynomial in question.  For example, if x is a repeated root that shows up as such twice, then that x value (root) has a multiplicity of 2.  If x shows up only once as a zero, it has a multiplicity of 1.  Does that fit in at all with what you've seen and learned?

campbell_st · Answer

show me where the sum of the multiplicities of a polynomial don't match the degree of the leading term...

campbell_st · Answer

ok... lets look at 

x = 0   multiplicity 2

x = 1  multiplicity 3

x = 5 multiplicity of 4

then 

$$f(x) = x^2(x -1)^3(x - 5)^4$$

what the degree of the polynomial...?

mathmale · Answer

That wasn't my point, Campbell.  I was saying that we need to determine how many times each distinct zero appears and and label each such zero with its individual multiplicity.  It does matter what the multiplicity of a zero is.  If I have my head screwed on right, the graph of a polynomial does not cross the x-axis when the multiplicity of that zero is even (e. g., 2).

mathmale · Answer

I agree completely with your assignment of multiplicity to each of the repeated roots of this polynomial.

campbell_st · Answer

the question is simply asking about the multiplicity of the roots... 

so 3 roots in a cube... there multiplicity is 1... 

why... the sum of the multiplicity is equal to the degree of the leading term... 

thats where I'm coming from... 

it may be quick and dirty.... but why do tedious maths when it isn't necessary

campbell_st · Answer

but then again I'm in high school... and not an university...

anonymous · Answer

so what your saying Campbell is the correct answer is b

campbell_st · Answer

sorry to carry on dog... but I hope we helped with your question

campbell_st · Answer

that would be my answer...(b)  multiplicity 1

anonymous · Answer

definintly your helping me a lot I would have never been able to figure it out on my own