SOLUTION: find all of the zeros of the polynomial function and state the multiplicity of each. f(x) = (x^2-9)^2 I don't really understand this.

Algebra ->  Average -> SOLUTION: find all of the zeros of the polynomial function and state the multiplicity of each. f(x) = (x^2-9)^2 I don't really understand this.      Log On


   

Question 189180: find all of the zeros of the polynomial function and state the multiplicity of each. f(x) = (x^2-9)^2
I don't really understand this.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If your equation has the form
f%28x%29+=+%28x+-+z%5B1%5D%29%28x+-+z%5B2%5D%29%28x+-+z%5B3%5D%29 etc.
then z%5B1%5D,z%5B2%5D,z%5B3%5D etc. are the zeroes
The multiplicity is the number of times a zero is repeated,
for instance:
f%28x%29+=+%28x+-+z%5B1%5D%29%5E3%28x+-+z%5B2%5D%29%28x+-+z%5B3%5D%29etc.
Zero z%5B1%5D has a multiplicity of 3, since it's
repeated 3 times
In your equation:
f%28x%29+=+%28x%5E2-9%29%5E2, I can factor it some more:
f%28x%29+=+%28%28x+%2B+3%29%28x+-+3%29%29%5E2
f%28x%29+=+%28x+%2B+3%29%28x+%2B+3%29%28x+-+3%29%28x+-+3%29
f%28x%29+=+%28x+%2B+3%29%5E2%28x+-+3%29%5E2
The zeroes are x+=+-3 multiplicity of 2
and x+=+3 multiplicity of 2 also