Question

What are the zeroes of the function? What are their multiplicities?
f (x) = 4x3 – 20x2 + 24x

Answer 1

\[4x^3 – 20x^2 + 24x=4x(x^2-5x+6)\]

is a start
then factor the quadratic to find the other two zeros

Answer 2

there will be 3 zeros, each with multiplicity 1

Answer 3

The numbers –3, –2, and 0 are zeroes of multiplicity 1.
The numbers 3, 2, and 0 are zeroes of multiplicity 2.
The numbers –3, –2, and 0 are zeroes of multiplicity 2.
The numbers 3, 2, and 0 are zeroes of multiplicity 1.

Answer 4

so which one would it be ?

Answer 5

yes. multiplicity means how many times a root is repeated.
notice in
4x*(x^2-5x+6)= 0
the x=0 makes this 4*0*(stuff) which will be 0
x=0 makes (x^2-5x+6) = 6 so x=0 works as a root only once.
so it is multiplicity 1.

if you had x*x =0 then either copy of x could be 0, and it is multiplicity 2

Answer 6

you can use the sum of roots = -b/a to check the remaining choices

you match x^2-5x+6 to ax^2 +bx +c and see a=1, b= -5
so -b/a= -(-5)/1= +5
the sum of the roots (other than 0) add to 5

Answer 7

so then it is either a or d...

Answer 8

so it's d?

Answer 9

or you could factor
x^2-5x+6

the + in +6 means both factors have the same sign
list the pairs of factors of 6
(1,6)
(2,3)
which pair add up to 5? 2,3
the sign of -5 (from -5x) says the biggest factor is negative, so both a -
we get (x-2)(x-3)=0
solve for the roots
x-2=0 or x=2
x-3=0 or x=+3

Answer 10

thanks (: