Question 144
Let
$$P(x)=x^4+ax^3+bx^2+cx+1,\qquad Q(x)=x^4+cx^3+bx^2+ax+1.$$
Find the conditions on the real parameters $a,b,c$ ($a\ne c$) for $P,Q$ to have two common roots, and solve $P(x)=0$ and $Q(x)=0$ in that case.
$$P(x)=x^4+ax^3+bx^2+cx+1,\qquad Q(x)=x^4+cx^3+bx^2+ax+1.$$
Find the conditions on the real parameters $a,b,c$ ($a\ne c$) for $P,Q$ to have two common roots, and solve $P(x)=0$ and $Q(x)=0$ in that case.