Answer
f(0) and f(1) have opposite signs,
so f(x) has a real zero between 0 and 1.
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=0,\quad f(a)=0^{3}-4(0^{2})+2=2\quad$(positive)
$ b=1,\quad f(b)=1^{3}-4(1^{2})+2=-1\quad$(negative)
f(0) and f(1) have opposite signs,
so f(x) has a real zero between 0 and 1.