Question

What are the zeros of the function? what are their multiplicities
f(x)=4x^3-20x^2+24x

numbers -3,-2,and 0 are multiplicity of 1
numbers 3,2,and 0 are multiplicity of 1

Answer 1

Common factor of

4 x ^ 3 - 20 x ^ 2 + 24 x
are 4x

4 x ^ 3 - 20 x ^ 2 + 24 x / 4
x =

x ^ 2 - 5 x + 6

OR


4 x ^ 3 - 20 x ^ 2 + 24 x = 4 x * ( x ^ 2 - 5 x + 6 )


4 x = 0 when x = 0

Solutions of equation :

x ^ 2 - 5 x + 6

are

x = 2 and x = 3


Solutions of equation :

4 x ^ 3 - 20 x ^ 2 + 24 x = 0

are

x = 0

x = 2 and

x = 3

Answer 2

thank you

Answer 3

When X=0, the function would be:

f(x) = 4x^3 -20x2 + 24x
0= 4x^3 -20x2 + 24x ----->divide all by x
x(4x^2 -20x + 24) =0 ------> split -20x into -12x and -8x
x(4x^2 -12x -8x + 24)
x{4x(x-3) - 8(x -3}
x(4x-8) (x-3)
x1= 0
x2= 8/4= 2
x3= 3