Find all integers n for which the equation x³ - 13x + n = 0 has three integer roots.

The only values of n for which the equation has all integer solutions are n=12 and n=-12.  The solutions for n=12 are -4, 1, and 3.

Using the discriminant criterion, there are three real solutions only if the integer n satisfies |n|<=18. Using an online solver 37 times will answer the question asked, then.

Posted by Richard on 2006-10-14 20:33:28