IMathAS-libretexts

Determine on which intervals, if any, $\displaystyle {f{{\left({x}\right)}}}$ will have a real zero, given:

$\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}-{67}{x}+{126}$

$\displaystyle {\left[-\frac{{7}}{{2}};-\frac{{3}}{{4}}\right]}$
$\displaystyle {\left[-\frac{{25}}{{4}};-\frac{{7}}{{2}}\right]}$
$\displaystyle {\left[\frac{{13}}{{4}};\frac{{9}}{{2}}\right]}$

$\displaystyle {\left[\frac{{5}}{{3}};\frac{{7}}{{3}}\right]}$
$\displaystyle {\left[\frac{{9}}{{2}};\frac{{23}}{{4}}\right]}$
None of the above.