Solve Quartic with Casio FX115MS

02042019, 01:39 PM
(This post was last modified: 08282019 01:21 AM by Albert Chan.)
Post: #3




RE: Solve Quartic with Casio FX115MS
(11292018 05:28 PM)Albert Chan Wrote: Example: f(x) = x^4 + 2 x^3 + 3 x^2 + 4 x + 5 = 0 Another way to calculate shifted polynomial coefficients is repeated synthetic divisions. Shift xaxis to k = 2/(4*1) = 0.5 k> 1 2 3 4 5 k> 1 1.5 2.25 2.875 3.5625 < C k> 1 1.0 1.75 2 < B k> 1 0.5 1.5 < A Repeated differentiations also work: C = f(k) = k^4 + 2 k^3 + 3 k^2 + 4 k + 5 = 3.5625 B = f'(k) = 4k^3 + 6k^2 + 6k + 4 = 2 A = f''(k)/2! = (12k^2 + 12k + 6) / 2! = 1.5 As expected: y^3 coef. = (24k + 12) / 3! = 0, y^4 coef. = (24) / 4! = 1 

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Messages In This Thread 
Solve Quartic with Casio FX115MS  Albert Chan  11292018, 05:28 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  11292018, 10:31 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  02042019 01:39 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  08242019, 12:47 PM
RE: Solve Quartic with Casio FX115MS  SlideRule  03142020, 01:28 AM
RE: Solve Quartic with Casio FX115MS  Albert Chan  08302019, 02:02 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  09022019, 02:35 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  02012020, 12:27 PM
RE: Solve Quartic with Casio FX115MS  Albert Chan  03132020, 06:30 PM

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