What are the zeroes of the function? What are their multiplicities?
f(x)=4x^3-10x^2+24x

a)The numbers -3,-2, and 0 are zeroes of multiplicity 1
b) the numbers 3,2, and 0 are zeroes of multiplicity 2
c)the numbers -3, -2, and 0 are zeroes of multiplicity 2
d) The numbers 3,2, and 0 are zeroes of multiplicity 1

Question

What are the zeroes of the function? What are their multiplicities?
f(x)=4x^3-10x^2+24x

a)The numbers -3,-2, and 0 are zeroes of multiplicity 1
b) the numbers 3,2, and 0 are zeroes of multiplicity 2
c)the numbers -3, -2, and 0 are zeroes of multiplicity 2
d) The numbers 3,2, and 0 are zeroes of multiplicity 1

campbell_st · Answer

well start every coefficient is even and every terms contains and x

so factor out 2x from each term 

which gives

$$f(x) =  2x(2x^2 - 5x + 12)$$

you now need to factor the quadratic... 

and can you see if you have entered the equation correctly

and the only roots shown as possible answers don't match the question

and the sum of the multiplicities need to match the degree of the polynomial... 

you have a cubic, degree 3... so if it has 3 roots.... they would all need to be mutiplicity 1 (1 +1 + 1 = 3). 

hope this helps.

anonymous · Answer

so would it be d?

campbell_st · Answer

well its A or D... 

but can you check your question and see if its not -20x    

you have - 10x