Answer
f(1) and f(2) have opposite signs,
so f(x) has a real zero between 1 and 2.
Work Step by Step
The Intermediate Value Theorem for Polynomial Functions$:$
Let $f$ be a polynomial function with real coefficients.
If $f(a)$ and $f(b)$ have opposite signs,
then there is at least one value of $c$ between $a$ and $b$ for which $f(c)=0$.
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$ a=1,\quad f(a)=1^{3}-1-1=-1\quad$(negative)
$ b=2,\quad f(b)=2^{3}-2-1=5\quad$(positive)
f(1) and f(2) have opposite signs,
so f(x) has a real zero between 1 and 2.
