SOLUTION: cind the zero of the polynomial function and stat the multiplicity of each. f(x)=x^4-18x^2+32 (the ^4 and ^2 are powers)

Algebra ->  Expressions-with-variables -> SOLUTION: cind the zero of the polynomial function and stat the multiplicity of each. f(x)=x^4-18x^2+32 (the ^4 and ^2 are powers)      Log On


   

Question 168496: cind the zero of the polynomial function and stat the multiplicity of each. f(x)=x^4-18x^2+32 (the ^4 and ^2 are powers)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E4-18x%5E2%2B32 Factor the trinomial and set the function equal to zero.
%28x%5E2-16%29%28x%5E2-2%29+=+0 Apply the zero product rule.
x%5E2-16+=+0 or x%5E2-2+=+0
If x%5E2-16+=+0 then x%5E2+=+16 so x+=+4 or x+=+-4
If x%5E2-2+=+0 then x%5E2+=+2 so x+=+sqrt%282%29 or x+=+-sqrt%282%29
The zeros are:
x+=+4
x+=+-4
x+=+sqrt%282%29
x+=+-sqrt%282%29
See the graph below as a confirmation.
graph%28400%2C400%2C-5%2C5%2C-50%2C35%2Cx%5E4-18x%5E2%2B32%29