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After having explained the underlying motivations, we study the location of the zeros of the functions  T ( z ) :=  Ae az +Be bz +Ce cz   of the complex variable  z  with complex coefficients  A ,  B ,  C  and real  a  &lt;  b  &lt;  c . As normal form of  T ( z )=0 serves the equation  e -pz/2 · sinh ( z /2)= P  with a complex parameter  P  and a real  p  ∈ (-1,1). The problem of finding all solutions  z  of this equation is reduced to the calculation of the unique solution in a horizontal fundamental strip  F  := {  z  ∈ C: - π  &lt; Im( z ) ≤  π  }. By detailed estimations, we find tight enclosures for the zero in  F . Series expansions and algorithms to find the zero  z  in  F  are propounded. A complete stability analysis for real trinomials is given. In a discussion, the problem is set into a wider perspective.

Enclosure, separation, and computation of the zeros of exponential trinomials with constant coefficients and real exponential points