2. Given that $m$ is a real number, and $\sin \alpha, \cos \alpha$ satisfy the quadratic equation $3 x^{2}-m x+1=0$ in $x$. Then $\sin ^{4} \alpha+$ $\cos ^{4} \alpha$ is ( ).
(A) $\frac{2}{9}$
(B) $\frac{1}{3}$
(C) $\frac{7}{9}$
(D) 1
2.C.

From the relationship between roots and coefficients, we know that $\sin \alpha \cdot \cos \alpha=\frac{1}{3}$. Therefore, we have
$$
\begin{array}{l}
\sin ^{4} \alpha+\cos ^{4} \alpha \\
=\left(\sin ^{2} \alpha+\cos ^{2} \alpha\right)^{2}-2(\sin \alpha \cdot \cos \alpha)^{2}=\frac{7}{9} .
\end{array}
$$