Let those roots be $x_1, x_2, ..., x_n$. We can draw $x_1 + x_2 + ... + x_n$ lines on the plane and partition them into $n$ sets $S_1$, $S_2$, ..., $S_n$ such that each set $S_i$ consists of $x_i$ parallel lines, no two lines from different sets are parallel, and no three lines are concurrent. Then the number of distinct intersection points made by lines from $S_i$ and $S_j$, where $i \neq j$, is exactly $x_ix_j$, and thus the total number of distinct intersection points is $\sum_{1 \leq i < j \leq n} x_ix_j$. But by Vieta this sum is equal to $b$ and $x_1 + x_2 + ... + x_n = a$, so this configuration of lines satisfy Baron's theorem. Hence it is true.