Math

What is the cubic formula?

I want one that will give me all three roots, not just one (for example, the quadratic formula has the +- sign so that whenever it is used for substitution, there will always be two results which are ultimately the two solutions). However, if you can find one without that, it's still okay.

Asked by sddh on 25 May 01:39

Last updated by anonymous on 25 May 17:53

1 Answers

Answered by mrmix55 on 25 May 17:53

Root[z|->a_0+a_1 z+a_2 z^2+a_3 z^3, k] = -a_2/(3 a_3)+(e^(2/3 i pi (k-1)) p)/(3 2^(1/3) a_3)-(2^(1/3) r)/(e^(2/3 i pi (k-1)) (3 p a_3)) for (p = (q+sqrt(q^2+4 r^3))^(1/3) and q = 9 a_1 a_2 a_3-2 a_2^3-27 a_0 a_3^2 and r = 3 a_1 a_3-a_2^2 and 1<=k<=3)