SOLUTION: Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2– 9)^2

Algebra ->  Expressions-with-variables -> SOLUTION: Find all of the zeros of the polynomial function and state the multiplicity of each. f (x) = (x^2– 9)^2      Log On


   

Question 147703: Find all of the zeros of the polynomial function and state the multiplicity of each.
f (x) = (x^2– 9)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f+%28x%29+=+%28x%5E2-9%29%5E2 Start with the given equation.


0+=+%28x%5E2-9%29%5E2 Plug in f%28x%29=0


0+=+%28x%5E2-9%29%28x%5E2-9%29 Expand.


x%5E2-9=0 or x%5E2-9=0 Set each factor equal to zero.


Let's solve the first equation x%5E2-9=0


x%5E2-9=0 Start with the given equation.


%28x%2B3%29%28x-3%29=0 Factor the left side.


x%2B3=0 or x-3=0 Set each factor equal to zero.


x=-3 or x=3 Solve for x.


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If we solve the second equation x%5E2-9=0, we will get the same answers x=-3 or x=3. So that means that both solutions occur twice. So the solutions are


x=-3 (with multiplicity of 2) or x=3 (with multiplicity of 2)