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It is easy to give an example of a polynomial of degree 3 with integer coefficients having:
(a) three distinct rational roots,
(b) one rational root and two irrational roots.
But for a while I am trying to construct one that all its roots are irrational but I can't. It seems that it is not possible at all?
Also, can a polynomial with integer coefficients of degree 3 have two rational roots and one irrational root?