if a and b are the roots of the quadratic equation x^2+x+1 then give the equation whos roots are a^14 and b^26

a=-b

a²=b²

a¹⁴=(a²)⁷=m⁷

b²⁶=(b²)¹³=(a²)¹³=m¹³

(x-m⁷)(x-m¹³)=0

x²-(m⁶+1)m⁷x+m²⁰

x²-(a¹²+1)a¹⁴x+a⁴⁰

a=w, b=w^2 where w is a complex cube root of unity

a^14 = w^14 = (w^12).(w^2) = w^2

b^26 = w^52 = (w^51)(w)=w

therefore, the required equation is

x^2 - (w+w^2)x + (w^3)=0

=>x^2 + x + 1=0, that is, the given equation....