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 - 14x^2 + 49x 
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^3-14x^2+49x

In order to find zeroes, we set f(x) = 0 and solve for x,

X^3-14x^2+49x = 0

x (x^2-14x+49) = 0

x(x-7)^2 = 0

Therefore, zeroes are at x = 0 and x = 7

Multiplicity of left most zero is 1

Multiplicity of right most zero is 2

At the left most zero the graph crosses x axis.

At right most zero the graph touches the x axis and turns around

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