Question 467867: 11. Find the real and complex zeros of the following function. Please show all of your work.
f(x)=x³-2x²+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)=x³-2x²+16
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f(x)=x³-2x²+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.
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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)
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(x³-2x²+16)/(x+2)=(x^2-4x+8)
f(x)=(x+2)(x^2-4x+8)
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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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