01-12-2019, 09:27 AM

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

Gamo

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

------------------------------------------------------

Remark:

This program is use to solve for "REAL ROOT"

-------------------------------------------------------

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.

-------------------------------------------------------

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

---------------------------------------------

-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

Gamo