Suppose p and q are odd integers.

Question

(a) Show that the quadratic equation x2 + px + q = 0 has no rational roots.
(A number á is a “root” of that equation if: á2 + pá + q = 0. A number is rational if it is expressible as
m/n for some integers m and n. )
(b) Does this result generalize to equations of the type xn + px + q = 0 ?