Real Computing Made Real
by Forman S. Acton · first published 1996
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From the book "real computing made real" by Acton, the suggestion is to first view (not always!) the quadratic as x^2 + 2bx + c, so its roots are -b +/- sqrt(b^2 - c). The product of the roots is c and therefore we can compute the root that…
on “The quadratic formula and low-precision arithmetic” ↗…unphysical artifacts of the discretization would wreck your calculation. Depending on how you did things rounding errors can be made better or worse, Foreman Action's Numerical Methods that Work and later Real Computing Made Real reveal techniques for managing these errors that let you accomplish a lot with floats and some would point out that going to doubles doesn't win you that much slack to do things wrong.
on “Building the System/360 Mainframe Nearly Destroyed IBM” ↗