Solution
= Solution
The given <polynomial root> supplies the factor $2x-3$. <Polynomial division> gives
$$
2x^3-5x^2+x+3=(2x-3)(x^2-x-1).
$$
Solving the remaining <quadratic equation>, the other two <polynomial roots> are
$$
\boxed{x=\frac{1+\sqrt5}{2}\quad\text{and}\quad x=\frac{1-\sqrt5}{2}.}
$$