The equation x5
+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.