Report Number: CS-TR-66-40
Institution: Stanford University, Department of Computer Science
Title: How do you solve a quadratic equation?
Author: Forsythe, George E.
Date: June 1966
Abstract: The nature of the floating-point number system of digital computers is explained to a reader whose university mathematical background is very limited. The possibly large errors in using mathematical algorithms blindly with floating-point computation are illustrated by the formula for solving a quadratic equation. An accurate way of solving a quadratic is outlined. A few general remarks are made about computational mathematics, including the backwards analysis of rounding error.
http://i.stanford.edu/pub/cstr/reports/cs/tr/66/40/CS-TR-66-40.pdf