Solution
= Solution
The known root gives a factor $x-1$ by the <factor theorem>. <Polynomial division> leaves $2x^2-7x+6=(2x-3)(x-2)$, so
$$
2x^3-9x^2+13x-6=(x-1)(2x-3)(x-2).
$$
Consequently all the roots are
$$
\boxed{x=1,\quad x=\frac32,\quad x=2.}
$$
The three linear factors account for the full degree of the <polynomial>, so there are no further complex roots.