Think of the graph of . If it means the polynomial is always increasing. Thus, it cross the x-axis precisely at one point. Let be therealroot of . Now if is the other root of then it has to be complex*. Thus, the final root is . The splitting field is . Note that by complex conjugation is an automorphism. Now there are three possibilities to send i.e. by isomorphism extension theorem. Call these maps . Then we see that .

*)You may want to say, but maybe has only real roots. But then it forces for some . However, is not larger than . So this is not possible.