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.
(In reply to Who needs p and q? (SPOILER)
by Old Original Oskar!)
There is a sign problem in the "Solving..." paragraph: for b=+/-1, then a=-2, or for b=+/-2, then a=-1, so a=-2 and b=-1, and the roots come to be -2 (twice), -1 (twice), and 6 (once).