Is a polynomial of degree 3 with irrational roots possible? [duplicate]
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite This question already has an answer here: Cubic polynomial with three (distinct) irrational roots 4 answers 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? algebra-precalculus elementary-number-theory share | cite | improve this question edited Oct 4 at 12:45 asked Oct 4 at 12:41 Edi 870 9 30 marked as duplicate by lulu, Winther, Holo, amWhy  algebra-precalculus Users with the  algebra-precalculus badge can single-handedly close algebra-precalculus questions as duplicates and ...