first tier second tier third tier fourth tier

past issues

2004 2003 2002 2001 2000 1999 1998 1997 1996 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Welcome to NRICH.

Formula for solving cubic equations

---

---

By Anonymous on Thursday, May 18, 2000 - 10:47 am:

Is there a general formula for solving cubic equations?

---

By Harry Smith (Harry) on Thursday, May 18, 2000 - 12:26 pm:

Yes there is! What you are referring to is an explicit solution, or solution by 'radicals'. You have probably seen this sort of solution when dealing with quadratics. For cubics, the formula is not as easily stated. It involves rewriting the formula in the form x³ + Ax = B. Rather than give all the details here, I'll refer you to cubic solution.

In fact you can solve any polynomial up to the fourth degree explicitly (or by radicals). The fact that the quintic (degree 5) is not in general soluble by radicals is the famous crowning glory of Galois Theory.

---