I’m trying to make a program for my TI-89 that finds the exact values of the roots of a cubic polynomial when all three are real and not equal. Is this even possible, and if so, how do I do it?
Hi.
Here is a page on my website that tells you how to find the roots of a cubic equation:
www.1728.com/cubic2.htm
and here’s a calculator that does it:
www.1728.com/cubic.htm
Umm… not necessary. Hit F2, and choose solve. Syntax for sample equation “x^3+x^2+x+1” would be:
“solve(x^3+x^2+x+1=0,x)”, without the quotes.
Yes, but that only gives approximate roots when they’re irrational.
What you want to do is possible, but not easy.
Um, all finite representations of irrationals are approximate. 
You could always use the Inverse Symbolic Calculator on your approximate numerical results.