Find the maximum roots for the given equation

For non-zero $a_{1}, a_{2}, . . . , a_{n}$ and for $b_{1}, b_{2},. . . , b_{n}$ such that $b_{i} ≠ b_{j}$ for $i ≠ j$ , the equation

$a_{1}e^{b_{1}x} + a_{2}e^{b_{2}x} +...+a_{n}e^{b_{n}x} = 0$

has at most $n-c$ real roots.

Then find c?