If $2+3i$ is one of the roots of the equation $2x^3-9x2+kx-13=0,$ k \in R$, then the real root of this equation

Question

$\begin{array}{1 1} \text{does not exist} \\ \text{exists and is equal to $\frac{1}{2}$} \\\text{exists and is equal to $\frac{-1}{2}$} \\ \text{exists and is equal to 1 } \end{array} $