Find the zeros of the given polynomial function f. State the multiplicity of each zero. (Order your zeros from smallest to largest, first by real part

Question

f(x) = (x² + 81)(x² − 3x + 2)²

 

I believe I have the correct answers but the online site won't take them.

I have x=1 multiplicity 2

          x=2 multiplicity 2

          x=-9i multiplicity 1

          x=9i multiplicity 1

Answer 1

First, completely factor the function.

 

f(x) = [(x - 9i)(x + 9i)] * [(x - 2)(x - 1)(x - 2)(x - 1)]

 

 

You only have 2 real distinct zeros:

 

x=1     and      x=2           each having a multiplicity of 2, because they appear twice.

 

The online site did not accept   x=-9i   and x=9i   as zeros because they are complex.  In other words, they are not solutions to f(x).