3. If the three roots of the equation $(x-1)\left(x^{2}-2 x+m\right)=0$ can be the lengths of the three sides of a triangle, then the range of the real number $m$ is ( ).
(A) $0 \leqslant m \leqslant 1$
(B) $m \geqslant \frac{3}{4}$
(C) $\frac{3}{4}<m \leqslant 1$
(D) $\frac{3}{4} \leqslant m \leqslant 1$
3. (C).

Let $\alpha, \beta$ be the roots of the equation $x^{2}-2 x+m=0$. From $\Delta=4-4 m \geqslant 0$, we get $m \leqslant 1$. Clearly, $\alpha+\beta=2>1$. Also, by the triangle inequality, which states that the difference of any two sides is less than the third side, we know $|\alpha-\beta|<\frac{3}{4}$. Therefore, the correct choice is
(C).