Let α be the common root of x3+ax+1=0 and x4+ax2+1=0 Then,α3+aα+1=0 and α4+aα2+1=0 subtracting both equations, α4−α3+aα2−aα=0 α(α3−α2+aα−a)=0 ⇒α2(α−1)+a(α−1)=0{α=0 doesn'[ give a root] ⇒(α−1)(α2+a)=0 ⇒α=1 or a=−α2 Clearly, α=1 gives a=−2 in both equations. Hence, for a=−2 both equation have a common root.