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#!/usr/bin/env octave
disp ("Solve quadratic equation a*x^3 + b*x^2 + c*x + d = 0");
a = input ("a = ");
while (a == 0)
disp ("a must be nonzero");
a = input ("a = ");
end
b = input ("b = ");
c = input ("c = ");
d = input ("d = ");
% Using the trigonometric and hyperbolic solutions on Wikipedia:
% https://en.wikipedia.org/wiki/Cubic_function
p = (3*a*c - b^2) / (3*a^2);
q = (2*b^3 - 9*a*b*c + 27*a^2*d) / (27*a^3);
if (p == 0)
disp ("The given cubic equation has only one distinct solution:");
x = cbrt(-q) - b/a/3
else
r = 2 * sqrt(-p/3);
disp ("The three solutions of the given quadratic equation are:");
for k = 0 : 2
x = r * cos((acos(3*q/p/r) - 2*pi*k) / 3) - b/a/3
end
end
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