The correct option is option (b) $3 \sqrt{2},-2 \sqrt{2}$

$f(x)=x^{2}-\sqrt{2} x-12=0$

$\Rightarrow x^{2}-3 \sqrt{2} x+2 \sqrt{2} x-12=0$

$\Rightarrow x(x-3 \sqrt{2})+2 \sqrt{2}(x-3 \sqrt{2})=0$

$\Rightarrow(\mathrm{x}-3 \sqrt{2})(\mathrm{x}+2 \sqrt{2})=0$

$\Rightarrow x=3 \sqrt{2}$ or $x=-2 \sqrt{2}$