If α,β  are the roots of x2−x +3=0 , then α4+β 4=

Given quadratic equation is x2−x +3=0 …… ( 1 ) If α,β  are the roots of Eq ( 1 ) then α+β=1, αβ = 3   (∵α+β=−ba,  αβ = ca) squaring on both side of α+β=1  ⇒α2+β2=(α+β)2−2αβ=1−6=−5 ∴ α4+β4=(α2+β2)2−2α2β2=25−18=7