Let K Be A Non Zero Integer Prove That The Polynomial P X X 3 X K 2 Has No Ratio
Let k be a non-zero integer. Prove that the polynomial p(x) = x^3 + x + k^2 has no rational roots as follows:
(a) Show that any rational root must be an integer.
(b) Show that any integer root m of p(x) must be a perfect square.
(c) Assuming (b), conclude that p(x) has no rational roots.