find the zeros for the given polynomial function and give the multiplicity for e

Question

find the zeros for the given polynomial function and give the multiplicity for each zero. state whether the graph crosses the x axis, or touches the x axis and turns around at each zero. 
f(x)=x^3 - 12x^2 + 36x 
a. the set of zeros is

b. multiplicity at the left most zero

c. multiplicity at the right most zero

d. complete the sentence 
at the left most zero....
1. the graph crosses the x axis 
2. the graph touches the x axis and turns around

e. complete the sentence 
at the right most zero....
1. the graph crosses the x axis 
2. the graph touches the x axis and turns around

Explanation / Answer

f(x)=x^3 - 12x^2 + 36x

x^3 - 12x^2 + 36x = 0

Take x out in common :
x(x^2 - 12x + 36) = 0

x(x - 6)(x - 6) = 0

x = 0 , 6 , 6

So, the answers are :
a. the set of zeros is 0 , 6

b. multiplicity at the left most zero : ONE

c. multiplicity at the right most zero : TWO

d.
at the left most zero....
The multiplicity is one, which is odd
and thus, it passes thru
"the graph crosses the x axis "

e.
at the right most zero....
The multiplicity is two, which is even
and thus, it
" touches the x axis and turns around"

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