一元三次方程

There several method!
Method 1: formula
For a cubic equation,

圖片參考：http://upload.wikimedia.org/math/0/6/3/0637b7e28a96a99cff153d4b20766e59.png

with a is non zero real number
and the root are x1 , x2 , x3


圖片參考：http://upload.wikimedia.org/math/3/4/8/348ffa4b63eb0ddd0c4391c9605e6865.png


Method 2: calculator
for casio fx-3650p, set the following programme in CMPLX mode
?→A: ?→B: ?→C: ?→M:

B÷3A→B: BCM-: B3 + M÷2A→M: B2 - C÷3A→C: M2 - C3→A:

√Abs Ans => Ans∠ . 5 arg A: Ans - M - 2Ans(Ans=M→A:

3√ Abs Ans => Ans∠3-1 arg A→A: Abs C => C÷A→C:

MM-: Lbl 0: 1∠ 5!oM: A Ans + C÷Ans-B◢ 2>MM+ => Goto 0: 0

for casio fx-5ofh, set the following programme in CMPLX mode
?→A: ?→B: ?→C: ?→D: B3 - 9┘2A( BC - 3DA→D: B2 - 3AC→C: D2 - C3→X:

√( Abs( Ans => Ans∠( . 5 arg(X: Ans - D - 2Ans(Ans=D→X:

3√( Abs(Ans => Ans∠(3-1 arg(X→X: Abs(C => C┘X→C:

For 0→D To 2: 1∠(5!oD: (X Ans + C┘Ans-B)┘(3A◢ Next for other types of calculator you can fine the programme by yourself


2011-07-31 07:37:28 補充：
if you don't want to use calculator , you can use remainder theorem to solve the cubic equation.