The equation x⁵ –23x³ –66x² +px +q =0 has three non-zero roots, and two of them are integers, with multiplicity 2.

Find p and q and determine all the roots of the given equation.

I acknowledge the short yet fully analytic and comprehensive solution to the problem which  was  submitted  by  Old Original Oskar! at the outset  with subsequent comments by Frederico Kereki.

I will be posting the solution to this problem in one week.

Posted by K Sengupta on 2006-06-15 03:33:42