9. (16 points) Let the real-coefficient polynomial
$$
P_{i}(x)=x^{2}+b_{i} x+c_{i}\left(b_{i}, c_{i} \in \mathbf{R}, i=1,2, \cdots, n\right)
$$

be distinct, and for any $1 \leqslant i<j \leqslant n, P_{i}(x)+$ $P_{j}(x)$ has exactly one real root. Find the maximum value of $n$.