Let $(x_k,y_k)$ be a set of $n$ point in the plane and consider $P$ the unique real polynomial of degree $n-1$ that interpolate those points, i.e. $P(x)=a_{n-1}x^{n-1}+\ldots+a_0$ satisfies $P(x_k)=y_k$ for $1\leq k\leq n$.
Question : Is there any caracterisation for the location of the (complex) roots of $P$ ? (Obviously, we assume $y_k\neq0$ for all $k$).