From: DBRS28A@prodigy.com (Mr. Gerald A. Sabin) Newsgroups: sci.math Subject: General solution to quartic (PLEASE) Date: 27 Jul 1998 12:27:32 GMT Solution to Quartic, Method I (known as the Ferrari method) The general quartic is, A4x^4 + A3x^3 + A2x^2 + A1x + A0 = 0 Eqn 1 where the Ai are real coefficients. Divide thru by A4 and get x^4 + B3x^3 + B2x^2 + B1x + B0 = 0 Eqn 2 complete the square by adding (Rx + S)^2 to both sides (x^2 + (B3/2)x + T/2)^2 = (Rx + S)^2 Eqn 3 R,S,T are constants yet to be determined. Collect coefficients of powers of x and equate them on both Eqn 2 and Eqn 3. R^2 = T + (B3^2)/4 - B2 Eqn 4 RS = B3*T/4 - B1/2 Eqn 5 S^2 = T^2/4 - B0 Eqn 6 Multiply Eqn 4 by Eqn 6 and equate result to (Eqn 5)^2 This yields an equation for T: T^3 - B2*T^2 +(B3*B1-4*B0)T - B1^2 - B3^2*B0 = 0 Eqn 7 At this point, the QUARTIC has been transformed into a CUBIC that needs to be solved. All of the above, plus the subsequent solution of the CUBIC can be written as a program in QBASIC. After that, you can solve QUARTICS all day long. Method II This is a Numerical Method that involves successive approximation. It is presented in Handbook of Mathematical Functions (AMS 55) by Abramowitz & Stegun Equation: X^4 + A*X^3 + B*X^2 + C*X + D = 0 we seek the quadratic factors (X^2 + P1*X + Q1) * (X^2 + P2*X + Q2) Assume a value for Q1, and divide it into D Make a computation to determine how to adjust Q1 and try again. ..etc... This method also is readily programmable by QBASIC. Best wishes, -Jerry email: Jerry_Sabin.NOSPAM@prodigy.com (remove .NOSPAM)