Expert: Richard J. Raridon - 6/29/2005

Question
Hello I am a tutor for high school and middle school algebra students. I have one student who is extremely bright and always asks the most intriguing questions. When I was explaining the formula that is the solution for the quadratic equation (you know, X= (-B+-Square Root(B^2-4AC))/2A) He asked me if there is a formula to solve equations of a higher order such as AX^3+BX^2+CX+D=O and so on. I must admit I had never thought of that, and it was not in his text book. So I told him I would find out. That's where you come in. Would you know the answer to this question? I would greatly appreciate it because as an algebra tutor, I like to think there is no algebra question that can stump me, but this one did.

thanks,

James Schendel

Answer
I don't know of any formula.  The way I solve equations like that is to re-write them as
f(x) = ax^3 +bx^2 +cx +d
and then put in a value for x and solve for f(x).  If x is a solution, then f(x)=0.  By trial and error you can find a solution if it has one.  If the solution is rational, such as x=e or 2x=3e, then you can divide the original equation by (x-e) or (2x-3e) and reduce the remaining fraction to a quadratic equation.