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

We know that, x 2+ x + 1 is a factor of ax3+bx2+cx+dHence, roots of x 2+ x + 1 are also roots of ax3+bx2+cx+d. Since, ω and ω2whereω=−12+3i2 are two complex roots  x 2+ x + 1Therefore, ω and ω2 are two complex roots of ax3+bx2+cx+dWe know that, a cubic equation has atleast one real root. Let real root be α. Then,α⋅ω⋅ω2=−da⇒α=−da