SOLUTION: Finding zeros of a function: f(x) = 1/2x^3 - x

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Question 163213: Finding zeros of a function:
f(x) = 1/2x^3 - x
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
To find the zeros of the function, you need to solve the equation:
%281%2F2%29x%5E3-x=0
Factoring the left side, we have
x%28%281%2F2%29x%5E2+-+1%29=0
So
x+=+0 or %281%2F2%29x%5E2-1=0
Solving %281%2F2%29x%5E2-1=0, we obtain:
%281%2F2%29x%5E2=1
x%5E2=2
x+=+sqrt%282%29 or x=-sqrt%282%29
So the zeros of the function are 0, sqrt%282%29 and -sqrt%282%29