Given equation, x3−x2−x−2=0 ⇒‌‌(x−2)(x2+x+1)=0 ∴α and β are ‌
−1±√3i
2
or we can say α and β are non-real complex roots of unity. So, let α=ω and β=ω2, where ω3=1 and ω2+ω+1=0 ∴α2020+β2020+α2020β2020 =ω2020+ω4040+ω2020ω4040