(12C Platinum) Cubic Equation

[Gamo]

ALG mode program solution of a Cubic Equation by Newton's Method.

f(x) = aX^3 + bX^2 + cX + d = 0

Successive approximations to a root are found by

Xi+1 = 2aXi^3 + bXi^2 -d / 3aXi^2 + 2bXi + c

Guess X0

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Remark:

This program is use to solve for "REAL ROOT"

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Procedure:

f PRGM // Each new program or GTO 000

a [R/S] b [R/S] c [R/S] d [R/S] X0 [R/S]

Display shown each successive approximation until root is found.

If more than one Real Solutions enter another guess and [R/S]

Maximum of 3 Real Root.

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Example:

x^3 - 4x^2 + 6x - 24 = 0

f [PRGM] or [GTO] 000
1 [R/S]
4 [CHS] [R/S]
6 [R/S]
24 [CHS] [R/S]
20 [R/S] // My starting guess
Display successive approximation search and stop when root is found.

Answer Display 4

X=4

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-2x^3 + 3x^2 + 4x - 5 = 0

f [PRGM] or [GTO] 000
2 [CHS] [R/S]
3 [R/S]
4 [R/S]
5 [CHS] [R/S]

10 [R/S] ...............display 1.8508
0 [R/S] .................display 1
5 [CHS] [R/S] ..........display -1.3508
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Program: ALG Mode

Code:


STO 0 R/S
STO 1 R/S
STO 2 R/S
STO 3 R/S
STO 4 x 2 x RCL 0 + RCL 1 x RCL 4 X^2 - RCL 3 ÷
(RCL 4 x 3 x RCL 0 + (RCL 1 x 2) x RCL 4 + RCL 2) = 
STO 5 - RCL 4 =
X=0
GTO 049
RCL 5
PSE
GTO 009
RCL 5
GTO 008

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