SOLUTION: Find the zeros of the polynomial x^6-4x^5+4x^4 Enter your answers in increasing order. Enter “none” in all entry areas if there are no zeros.

Algebra ->  Finance -> SOLUTION: Find the zeros of the polynomial x^6-4x^5+4x^4 Enter your answers in increasing order. Enter “none” in all entry areas if there are no zeros.       Log On


   

Question 1014897: Find the zeros of the polynomial
x^6-4x^5+4x^4
Enter your answers in increasing order. Enter “none” in all entry areas if there are no zeros.
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the zeros of the polynomial
x^6-4x^5+4x^4
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Factor x%5E4 out of parentheses:

x^6-4x^5+4x^4 = x%5E4%2A%28x%5E2+-+4x+%2B+4%29.

Next, x%5E2+-+4x+%2B+4 = %28x-2%29%5E2.

The roots of the original polynomial are x=0 of multiplicity 4 and x=2 of multiplicity 2.