Abstract
The article proposes a new simple method for localizing and determining the number of real solutions for an arbitrary trinomial algebraic equation with real coefficients. In detail, with illustrations, an analysis is made of all types of equations under study. For each type, conditions for the existence of multiple roots are obtained and exact analytical formulas for calculating them are given. For trinomial equations with a multiple root, it is shown that all other roots can be expressed through a multiple with the required accuracy.
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