If α,β  are the roots of x2−2x+4=0 , then α4+β4 =

The given equation is x2−2x+4=0 α,β  are the given rootsSum of the  roots : α+β=2,      Product of the roots : αβ=4 α4+β4=(α2+β2)2−2α2β2          (∵a4+b4=(a2+b2)2−2a2b2) Here α2+β2=(α+β)2−2αβ=4−8=−4 α4+β4=(α2+β2)2−2α2β2=16−32=−16