math-intergral upper bound

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This one has me stumped.
Find the least integral upper bound of the zeros of the function f(x)=x^3-x^2+1

So by the rational root theorem, 1 and -1 might be roots.
by using synthetic division, i get the following values:
for f(-1)=-1
f(0)=1
f(1)=1
f(2)=5

and there is changes in the signs of the remainder/quotient for -1 and 0, but no changes for 1 and 2.

So would 1 be the upper bound, or 2?
Thanks for the help.

  • math-intergral upper bound -

    after-thoughts:
    the only real zero is negative, so I guess would 0 be the upper bound? maybe? lol

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