Imagine the Universe!
Imagine Home | You Be the Astrophysicist! |

Solution to a Cubic Equation

Cubic equations are polynomial equations of the form x3 + ax2 + bx + c = 0.

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

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

  • Q = (3b-a2)/9
  • R = (9ab - 27c - 2a3)/54

From these, compute

  • S = (R + sqrt(Q3 + R2))1/3
  • T = (R - sqrt(Q3 + R2))1/3

Then the real solution is

x1 = S + T - a/3.

Return Click here return to solve for the mass of Cygnus X-1.
Tools Click here for more help in solving for the mass of Cygnus X-1.

Imagine the Universe is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center.

The Imagine Team
Acting Project Leader: Dr. Barbara Mattson
All material on this site has been created and updated between 1997-2012.

DVD Table of Contents
Educator's Index