ILL 1989 Problem 84

Let $n \in \mathbb{Z}^+$ and let $a, b \in \mathbb{R}.$ Determine the range of $x_0$ for which

$$\sum^n_{i=0} x_i = a \text{ and } \sum^n_{i=0} x^2_i = b,$$

where $x_0, x_1, \ldots , x_n$ are real variables.