SOLUTION: 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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Question 1014681: 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.

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
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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Factor out :

 = .

Now solve this polynomial equation:

 = .

Its 3 roots are x = 0 of multiplicity 3.

Next you need to solve this quadratic equation 

 = .

Notice that the left side is .

So, your equation is 

 = .

It has the root x = 3 of multiplicity 2.

Answer. The roots are x=0 of multiplicity 3 and x=3 of multiplicity 2.


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