TI-BASIC:Cubic Formula
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Routine Summary
Solves for the complex roots of a cubic equation.
Inputs
A, B, C, D - the constants in Ax^^3^^+Bx^^2^^+Cx+D=0
Outputs
The three roots (or repeated roots)
Variables Used
A, B, C, D, M, N, O, P, Q, R, U, V, W
Calculator Compatibility
TI-83/84/+/SE Author
theFlyingDutchmanURL: United TI Download
ClrHome Disp "AX³+BX²+CX+D=0 Prompt A,B,C,D √((2B³-9ABC+27A²D)²-4(B²-AC)³→M 2B³-9ABC+27A²D→R ³√(0.5(R+M→N ³√(0.5(R-M→O (1+i√(3))/6A→P (1-i√(3))/6A→Q -B/(3A)-N/(3A)-O/(3A→U -B/(3A)+PN+QO→V -B/(3A)+QN+PO→W Disp "X1=",U Disp "X2=",V Disp "X3=",W
This is the complete program used to give the three roots that solve the cubic equation. If there are less than 3 roots, it will still give three answers. Because the formula used to solve cubic equations is quite big, several repeated parts are turned into variables.
