Re: Quadratic formula program help Message #18 Posted by Palmer O. Hanson, Jr. on 16 June 2012, 10:53 p.m., in response to message #5 by Paul Dale
In late 2008 I was working with Rodger Rosenbaum on testing of quadratic solvers and wrote
Quote:
None of those cases [in the Cadillac writeup] actually test the capability to run 24 digits. I located the test case that I devised to test for 24 digits capability and ran it successfully. The details are:
a = 456,987,654,328 b = -913,975,308,642 c = 456,987,654,314
R1 = 1. ; R2 = 1 - 14/a = 0.9999999999693645...
Both the HP-33s and the HP-35s will display the solution as two equal roots of 1.000000000 in Fix 9, but use of the Show function will reveal that one of the roots is actually calculated as 0.999999999969
The discriminant for the standard quadratic formula is 196, but since the internal solution is made with the revised formula ax^2 - 2bx + c the discriminant calculated by these programs is 49 .
I will be adding that test case to the Cadillac article.
But I note that I never did add the test case to the article. Maybe that was an early indication of things to come where recently I was unable to remember that Grand Forks is in North Dakota not in Minnesota.
I was also doing some work with my TI-89 using the approximate and exact modes. Again, from some correspondence with Rodger:
Quote:
I have been doing a little work with my TI-89. If I enter
zeros(456987654328x^2+913975308642x+456987654314,x)
then in the approximate mode I get 9999999776328 and 1.00000022359 which is not correct. But in exact mode I get
228493827157/228493827164 and 1 which is correct.
I presume that the same thing can be done in the HP-49 and HP-50 which I believe also have exact mode.
So I conclude that machines which have exact mode don't need a special quadratic routine which will calculate an extended version of the discriminant. But for the other machines such as the HP-33s, HP-35s, HP-28 anf HP-48 whhich can't do exact calculations then one of the 24 digit discriminant calculation capabilities is appropriate.
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