If p is a real number,a should be real,ff(x) is a polynomial with real with real coeficients.So,their roots are conjegate,ff's degree is 4,only 5 is real roots,5 has to be repeated,contradiction.
Sometime I'm a little bit stubborn as being a teacher too long,...I think I'm right to "saing to go".
You said I HUTU,in fact,I too care.