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.

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