## College Algebra (6th Edition)

$f(2)$ and $f(3)$ have opposite signs, so f(x) has a real zero between $2$ and $3$.
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 $f(c)=0$. ------------------- $a=2,\quad f(a)=(2)^{4}+6(2)^{3}-18(2)^{2}$ $=16+48-72=-8\quad$(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 $3$.