设二次型 $f\left(x_1, x_2, x_3\right)=\boldsymbol{x}^{\mathrm{T}} \boldsymbol{A} \boldsymbol{x}=x_1^2+5 x_2^2+x_3^2-4 x_1 x_2+2 x_2 x_3$, 则对任意的三维向量 $\boldsymbol{x}=\left(x_1, x_2, x_3\right)^{\mathrm{T}} \neq \mathbf{0}$, 均有
$\text{A.}$ $f\left(x_1, x_2, x_3\right)>0$.
$\text{B.}$ $f\left(x_1, x_2, x_3\right) \geqslant 0$.
$\text{C.}$ $f\left(x_1, x_2, x_3\right) < 0$.
$\text{D.}$ $f\left(x_1, x_2, x_3\right) \leqslant 0$.