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Solving a Cubic Equation

You might remember solving quadratic equations in middle school using the quadratic formula. Cubic equations can be solved with a similar formula, though the formula is a bit more complicated.

Cubic equations are polynomial equations of the form:

x^3 + ax^2 + bx + c = 0

Cubic equations have three possible values for x, at least one of which is real. Below are the equations necessary for finding the real root.

First compute the following two quantities from the coefficients a, b, and c:

Q=(3b-a^2)/9
(9ab - 27c - 2a^3)/54

From these, compute the following:

S = (R + sqrt(Q3 + R^2))^(1/3)
T = (R - sqrt(Q3 + R^2))^(1/3)

Then the real solution is:

x1 = S + T - a/3

More Information Get a bit more help in solving this equation

More Information Return to solving the binary equation for the black hole mass

More Information Return to the beginning and try another approach