Answer
$f(2)$ and $f(3)$ have opposite signs,
so f(x) has a real zero between $2$ and $3$.
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=2,\quad f(a)=(2)^{4}+6(2)^{3}-18(2)^{2}$
$=16+48-72=-8\quad$(negative)
$ b=3,\quad f(b)=(3)^{4}+6(3)^{3}-18(3)^{2}$
$=81+162-162=81\quad$(positive)
$f(2)$ and $f(3)$ have opposite signs,
so f(x) has a real zero between $2$ and $3$.
