Restrictions proving quasiconcavity of utility function
Since $u$ is twice differentiable, it is quasi-concave if and only if its marginal rate of substitution declines as $x_1$ increases and $x_2$ falls. You can then compute
$$
MRS = \frac{\frac{\partial u}{\partial x_1}}{\frac{\partial u}{\partial x_2}} = \frac{1}{\gamma x_2^{\gamma - 1}} = \frac{x_2^{1 - \gamma}}{\gamma};
$$
which is increasing in $x_2$ (so quasi-concave) if and only if $\gamma &lt; 1$. [We assume throughout that $\gamma &gt; 0$ since $u$ is increasing.]