SOLUTION: 11. Find the real and complex zeros of the following function. Please show all of your work. f(x)=x�-2x�+16 please help. thank u!

Question 467867: 11. Find the real and complex zeros of the following function. Please show all of your work.
f(x)=x�-2x�+16
please help. thank u!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the real and complex zeros of the following function. Please show all of your work.
f(x)=x�-2x�+16
...
f(x)=x�-2x�+16
If you are allowed to use a graphing calculator you will find that the given function has only one rational real root=-2. I could have used the rational roots theorem, but I don't know how to show you the procedure with this format.
..
Divide f(x) by (x+2) by long division or by -2 using synthetic division. (again, this format doesn't allow me to show you how to do this)
..
(x�-2x�+16)/(x+2)=(x^2-4x+8)
f(x)=(x+2)(x^2-4x+8)
..
x^2-4x+8=0
completing the square
(x^2-4x+4)+8-4=0
(x-2)^2=-4
take sqrt of both sides
x-2=�√-4
x=2�√-4=2�2i
f(x)=(x+2)(2+2i)(2-2i)
This function has one real root and 2 imaginary roots
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