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\begin{document}

\title{The Ins and Outs of Solving Quadratic Equations with Floating-Point
Arithmetic}



\author[1]{Frédéric Goualard}%
\affil[1]{Nantes Universite}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{abstract}
Solving quadratic equations with radicals on a computer with
floating-point arithmetic requires great care to handle correctly all
possible parameters. Literature on the subject glosses over the details,
often considered as important but tedious to present. As a consequence,
most implementations are flawed in one way or another. After having
reviewed both the literature and the actual implementations in several
programming languages and applications, we present an algorithm inspired
from an exposition by Pat Sterbenz from 1974, adapted to take advantage
of more recent researches in the field, which leads to a robust
quadratic equation solver.%
\end{abstract}%



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