I want to find the zeroes for functions that look like this (an example):$$f(t) = k_1e^\left(a_1t\right)+k_2e^\left(a_2t\right)+k_3e^\left(a_3t\right) ,$$where all $a_i$ are negative real numbers, so this sum always converges to zero at infinity. With two factors of $k$, I can simply compare both and solve it algebrically. However, I am stuck with how to do it with 3 or more factors. This may probably be a stupid question, but it doesn't ring any bells and I couldn't find anything related on a web search.
Thank you.