b. $3x^2 -2m\sqrt 3 x +1 >0 \quad \forall x \in \mathbb R$$\Leftrightarrow \begin{cases}a=3>0 \\ \Delta'=27m^2-3<0 \end{cases}\Leftrightarrow -1/3
b. $3x^2 -6m\sqrt 3 x +1 >0 \quad \forall x \in \mathbb R$$\Leftrightarrow \begin{cases}a=3>0 \\ \Delta'=27m^2-3<0 \end{cases}\Leftrightarrow -1/3<m<1/3.$
b. $3x^2 -
2m\sqrt 3 x +1 >0 \quad \forall x \in \mathbb R$$\Leftrightarrow \begin{cases}a=3>0 \\ \Delta'=27m^2-3<0 \end{cases}\Leftrightarrow -1/3