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Trace: • DM41X Polynomial Solver

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DM41X Polynomial Solver

Advantage Pac Polynomials

Assuming Advantage Pac is plugged in…

Finds all roots, including complex ones.

Save to registers

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

Roots of a quadratic

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

Higher order with complex roots

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

Cube Roots of minus 8

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

Further Information

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Page updated : 16/02/26 08:51 GMT


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