Question 1014681
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Find the zeros of the polynomial x^5-6x^4+9x^3.

Enter your answers in increasing order. Enter “none” in all entry areas if there are no zeros.
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<pre>
Factor out {{{x^3}}}:

{{{x^5-6x^4+9x^3}}} = {{{x^3*(x^2-6x+9)}}}.

Now solve this polynomial equation:

{{{x^3*(x^2-6x+9)}}} = {{{0}}}.

Its 3 roots are x = 0 of multiplicity 3.

Next you need to solve this quadratic equation 

{{{x^2-6x+9}}} = {{{0}}}.

Notice that the left side is {{{(x-3)^2}}}.

So, your equation is 

{{{(x-3)^2}}} = {{{0}}}.

It has the root x = 3 of multiplicity 2.

<U>Answer</U>. The roots are x=0 of multiplicity 3 and x=3 of multiplicity 2.
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