DM41X Polynomial Solver

** Advantage Pac Polynomials **

Assuming Advantage Pac is plugged in…

Finds all roots, including complex ones.

To save the discovered roots in registers

• Enter the polynomial coefficients as normal
• prior to pressing RT to do the solve SET FLAG 06
  • ShiftSF06
• This will save the discovered roots in R24 upwards
  • saves in pairs as REAL and IMAGINARY
    • R24 = REAL root 1
    • R25 = IMAG root 1
    • R26 = REAL root 2
    • R27 = IMAG root 2
    • etc
    • etc

To find the roots of a simple quadratic (with 2 real roots)

'' x² - 3x + 2 = 0 ''

• XEQ ALPHAPLYALPHA
• Asks for DEGREE=?
  • this is the highest power of x in the polynomial
  • enter 2 R/S
• Asks for a2=?
  • the coefficient of x2
  • enter 1 R/S
• Asks for a1=?
  • the coefficient of x
  • enter 3 CHS R/S
• Asks for a0=?
  • the constant term
  • enter 2 R/S
• Display shows FX RT NEW
  • FX = Function value at your choice of x
  • RT = Root(s) of the entered polynomial
  • NEW = Enter a new polynomial
  • Choose RT B
• Display shows ROOT = 2.0000
  • to see next root press R/S
• Display shows ROOT = 1.0000

The roots of our quadratic are 2 and 1

Either press TAN (J) to get the menu, and then NEW (LN) or XEQ PLY again

'' 4x⁴ - 8x³ - 13x² - 10x + 22 = 0 ''

This should have 4 roots, and most likely some will be complex.

• DEGREE=?
  • 4 R/S
• a4=?
  • 4 R/S
• a3=?
  • 8CHSR/S
• a2=?
  • 13 CHSR/S
• a1=?
  • 10 CHSR/S
• a0=?
  • 22R/S
• FX RT NEW
  • RT B

Roots are displayed:

• U = -1.0000 R/S
• V = 1.0000 R/S
• U = -1.0000 R/S
• V = -1.0000 R/S
• ROOT = 3.1180 R/S
• ROOT = 0.8820 R/S
• FX RT NEW

The 4 roots are

• ''-1 + j 1 ''
• '' -1 - j 1 ''
• '' 3.1180 ''
• '' 0.8820 ''

If x is the cube root of minus 8 then '' x³ = -8 '' and as a polynomial '' x³ + 8 = 0 ''

Simply use 0 as the coefficient of X² and x

• XEQ ALPHAPLYALPHA
• Degree=? 3 R/S
• a3=? 1 R/S
• a2=? 0 R/S
• a1=? 0 R/S
• a0=? 8 R/S

• RT B
  • ROOT = -2.0000 R/S
  • U = 1.0000 R/S V = 1.7321
  • U = 1.0000 R/S V = -1.7321

• Roots are
  • '' 2.0000 ''
  • '' 1 + j 1.7321 ''
  • '' 1 - j 1.7321 ''

— John Pumford-Green 26/01/26 09:55 GMT

Page updated : 19/04/26 21:11 BST