DM32 Polynomial Solver

** From the Owner's Manual **

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

Local copy polyroot.d32

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

'' 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
• 1^st root is shown
  • X=1.0000 R/S
• 2^nd root is shown
  • X=2.0000 R/S
• quits

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

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 + j1
• X = 1 - j1

'' 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
• C

The three cube roots of -8 are

• -2
• '' 1 + j1.73205 ''
• '' 1 - j1.73205 ''

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

Page updated : 19/04/26 21:09 BST