Dears,
Let $f(x):=1+\sum_{k=1}^{n}a_{i}b_{i}^{k}$, for each $x\in[a,b]$, where $a_{i}$ are real numbers (not nulls) and $b_{i}>0$. Assume that $f$ has, at least, two ceros in $[a,b]$. Then, I want to estimate the minimal distance between two consecutive zeros of $f$.
Somebody know some result (paper, book, ...) related with this question? Or, How do you think can be processed this issue?
Thank for your time.