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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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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.