<-[[.:start]] ====== 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 {{ :public:calculator:guides:polyroot.d32 |}} ===== Use ===== 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. ==== 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 * 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'' ==== 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 = 1.0000''R/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'' === 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 * 'C' The three cube roots of ''-8'' are * ''-2'' * '' 1 + j1.73205 '' * '' 1 - j1.73205 '' ===== Further Information ===== {{tag>calculator dm32}} Page created : 17/04/26 09:41 BST Page updated : ~~LASTMOD~~