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←Hints & Tips

DM32 Polynomial Solver

** From the Owner's Manual **

State File

Provided by Swiss Micros https://technical.swissmicros.com/dm32/examples/STATE/POLYROOT.d32

Local copy polyroot.d32

Use

This set of programs will provide real and complex roots of polynomials up to 5th order. The coefficient of the highest term is assumed to be 1 and all the coefficients must be normalized to make this so.

Quadratic

'' x2 - 3x + 2 = 0 ''

  • Run XEQ P
  • Enter the order at the prompt for F? '' * 2 R/S * Enter coefficient ''B
    • 3 +/- R/S
  • Enter coefficient A
    • 2 R/S
  • 1st root is shown
    • X=1.0000 R/S
  • 2nd root is shown
    • X=2.0000 R/S
  • quits

The two roots of '' x2 - 3x + 2 = 0 '' are 1 and 2

4-th order

4x4 - 8x3 - 13x2 - 10x + 22 = 0

This has a non-unity value for the highest term, so all the coefficients need to be divided by 4 to make it so, this can be done as they are entered

  • XEQ P
  • Enter order 4 at the prompt for F? '' * 4 R/S * Enter the coefficients starting at the second one (for x3) and dividing by 4 * 8 +/- ENTER 4 ÷ R/S * 13 +/- ENTER 4 ÷ R/S * 10 +/- ENTER 4 ÷ R/S * 22 ENTER 4 ÷ R/S * The first root is shown * ''X = 0.88197 R/S
  • The second root is shown
    • X = 3.11803 R/S
  • The third root is shown (it's complex)
    • X=-1.0000 R/S
    • i = 1.0000R/S
  • The fourth root is shown (it's also complex)
    • X=1.0000 R/S
    • i=-1.0000 R/S
  • C

The 4 roots are

  • X = 0.88197
  • X = 3.11803
  • X = -1 + i1
  • X = 1 - i1

Cube roots of -8

'' X3 = -8''

'' X3 + 8 = 0 ''

  • XEQ P
  • Enter 3 for the order
    • 3 R/S
  • Enter zero for C (the coefficient of x2)
    • 0 R/S
  • Enter zero for B (the coefficient of x)
    • 0 R/S
  • Enter 8 for A (the constant term)
    • 8 R/S
  • The first root is
    • X = -2.00000 R/S
  • The second root is complex
    • '' X = 1.00000'' R/S
    • i = 1.73205 R/S
  • The third root is complex
    • X = 1.0000 R/S
    • i = -1.73205 R/S
  • Ctrl

The three cube roots of -8 are

  • -2
  • '' 1 + i 1.73205 ''
  • '' 1 - i 1.73205 ''

Further Information

Page created : 17/04/26 09:41 BST

Page updated : 17/04/26 10:09 BST