# TI-BASIC:Cubic Formula

From Learn @ Cemetech

**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**

theFlyingDutchman*URL:* 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.