|Re: Rootfinding function (SOLVE) and guesses|
Message #14 Posted by Karl Schneider on 6 Aug 2010, 2:56 a.m.,
in response to message #13 by Don Shepherd
Personally, I'd like the solver to do this for a quadratic equation: recognize that it's a quadratic, get the coefficients of x^2 and x and the constant term (a, b, and c), apply the quadratic formula, and return the two solutions (if there are two solutions) in x and y.
This requires that the equation be entered in full detail. And, what if the terms had not been gathered -- should the calc still be able to recognize it as a quadratic? Any sophisticated solution will entail CAS.
I still say that the ideal solution is a polynomial solver, like that of the HP-48G and its descendants: Choose "Solve Polynomial" from the SOLVE menu, enter [1 5 6], hit "Solve", and read -2 and -3 as the answers. A PC might be a better tool if the problem is more complicated than that.
A quadratic-equation problem came up at work recently. After failing for a short while at simply reckoning an operating point, I derived a quadratic expression, programmed it as an equation on the HP-32SII, and quickly solved it numerically, knowing what a realistic answer would look like. (The other solution, which I computed manually, was indeed unrealistic -- well outside the operating limits of the equipment. The HP-32SII found that one, too, with suitable guesses steering it in that direction.)
Edited: 8 Aug 2010, 2:21 a.m. after one or more responses were posted