(12C Platinum) Cubic Equation
02-04-2019, 04:10 PM (This post was last modified: 09-02-2019 08:52 PM by Albert Chan.)
Post: #3
 Albert Chan Senior Member Posts: 2,555 Joined: Jul 2018
RE: (12C Platinum) Cubic Equation
Another way to get good guess is "look" at shape of curve

Example 1: x^3 - 4x^2 + 6x - 24 = 0
x((x-2)² + 2) = 24 ~ 2.88³

Any guess > 2 work. Say, guess = 3
X = 3 -> 4.6667 -> 4.1220 -> 4.0051 -> 4.0000

Example 2: -2x^3 + 3x^2 + 4x - 5 = 0
x^3 - 1.5x^2 - 2x + 2.5 = 0
x((x-0.75)² - 2.5625) = -2.5 ~ -1.36³

If RHS is 0, we have roots -0.8508, 0, 2.3508, with LHS interval signs = - + - +
Any guess < -0.8508 work. Say, guess = -1.5
X = -1.5 -> -1.3649 -> -1.3509 -> -1.3508

Since LHS interval (0, 2.3508) also is negative, eqn might have 3 real roots.
Indeed it does, 3 roots = -1.3508, 1.0000, 1.8508
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 Messages In This Thread (12C Platinum) Cubic Equation - Gamo - 01-12-2019, 09:27 AM RE: (12C Platinum) Cubic Equation - Albert Chan - 01-12-2019, 01:39 PM RE: (12C Platinum) Cubic Equation - Albert Chan - 02-04-2019 04:10 PM RE: (12C Platinum) Cubic Equation - Thomas Klemm - 02-04-2019, 08:13 PM RE: (12C Platinum) Cubic Equation - Albert Chan - 02-05-2019, 10:24 PM RE: (12C Platinum) Cubic Equation - Gamo - 02-05-2019, 04:24 AM RE: (12C Platinum) Cubic Equation - Thomas Klemm - 02-05-2019, 06:09 AM RE: (12C Platinum) Cubic Equation - Thomas Klemm - 02-05-2019, 06:20 AM

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