<-[[.:start]] ====== 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** * ShiftSF''06'' * 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=?'' * ''8''CHSR/S * ''a2=?'' * ''13'' CHSR/S * ''a1=?'' * ''10'' CHSR/S * ''a0=?'' * ''22''R/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 ===== {{tag>calculator dm41x}}