Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have:

$$ x^3 -2k^2x - k^2 = 0 $$

Now, I want to factor it so that I can easily solve for $x$, as you can see I cannot directy use quadratic formula. AFAIK, I am expecting 3 terms here like $(a-x)(b-x)(c-x)=0$. Thanks in advance and more power.

share|cite|improve this question
up vote 3 down vote accepted

Since it is in the form of a monic depressed cubic (leading coefficient=1 and no quadratic term), Cardano's method is a good way to go to find the solutions. Unfortunately, for arbitrary $k,$ the solutions aren't pretty, so the factorization is not going to be easily done.

share|cite|improve this answer

You should check on cubic polynomials. Yours is the special case of a depressed cubic, the details of the solution method are given in the linked Wikipedia entry. My tame computer algebra system maxima gives the three roots, they are a veritable mess.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.