Determine all possible pairs (P,Q) of positive integers such that each of the roots of:
X^{3}  17X^{2} + Px  Q^{2} = 0 is an integer.
(In reply to
No Subject by armando)
By the rule of signs the equation will have no negative roots.
The sum of the roots is 17 and checking the few possibilities gives four values for roots, P, Q:
(1,8,8), 80, 8
(2,5,10), 80, 10
(3,6,8), 90, 12
(4,4,9), 88, 12

Posted by xdog
on 20160424 10:26:19 