Quadratic Solver for Casio FX-3650P
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11-09-2018, 06:43 PM
(This post was last modified: 04-10-2019 10:10 PM by Albert Chan.)
Post: #7
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RE: Quadratic Solver for Casio FX-3650P
Another way to get discriminant, from Kahans cubic equation paper (page 11)
BTW, page 12 example 2 typo, should be: 1,160,928,203² - 3,234,424,451 * 416,690,636 = -89,060,331,627 PHP Code: function b2_less_ac(a, b, c) -- assume a, c > 0 To show that reduction code work, let reduced a = a', reduced b = b': b'² = (b - nc)² = b² - nc * (2b - nc) = b² - nc * (b+b') a'c = (a - nb - nb') * c = ac - nc * (b+b') -> b'² - a'c = b² - ac lua> A, B, C = 8441600, -22222222, 14624809 -- previous post example lua> verbal = true lua> b2_less_ac(4*A, B, C) 22222222² - 33766400 * 14624809 7027396² - 14624809 * 3376748 273900² - 3376748 * 22217 7296² - 22217 * 2396 108² - 2396 * 5 2² - 64 * 5 -316 Doing by hand, we can do slightly better: (-22222222)² - (4)(8441600)(14624809) = 22222222² - (5849923600)(84416) -- n = round(22222222/84416) = 263, b' = b-nc = 20814 = 20814² - (84416)(5849923600 - 263*22222222 - 263*20814) = 20814² - (84416)(5132) = -316 |
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Messages In This Thread |
Quadratic Solver for Casio FX-3650P - Albert Chan - 07-17-2018, 04:29 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 07-17-2018, 10:52 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 07-18-2018, 04:35 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 08-10-2018, 04:28 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 08-11-2018, 02:29 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 08-11-2018, 10:13 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 11-09-2018 06:43 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 11-10-2018, 08:14 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 11-11-2018, 05:44 PM
RE: Quadratic Solver for Casio FX-3650P - Albert Chan - 12-03-2018, 12:08 PM
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