If x2+x+1  is a factor of ax3+bx2+cx+d then the real root of ax3+bx2+cx+d=0 is,

It is given that x2+x+1 is a factor of ax3+bx2+cx+d But  x2+x+1=0  has its roots as ω  and  ω2.   . So, two imaginary roots ofax3+bx2+cx+d=0  are ω  and   ω2. Let the third real root be  αThen,    ωω2α=(−1)3da⇒α=−daHence, the real root of   ax3+bx2+cx+d=0  is  −da.