1
Question
lf α, β are the roots of x2−x+1=0 then α5+β5=
lf α, β are the roots of x2−x+1=0 then α5+β5=
Open in App
Solution
The correct option is C 1
α,βaretherootsoftheequationx2−x+1⇒x=1−i√32or1+i√32∴α=−ωandβ=−ω2whenω3=1Nowα5=−ω5andβ5=−(ω2)5=−ω3.w2=−ω2=−ω3ω3ω3ω=−ω∴α5+β5=−ω2−ω=−(ω2+ω)=−(−1)=1∴OptionB(Ans)
α,βaretherootsoftheequationx2−x+1⇒x=1−i√32or1+i√32∴α=−ωandβ=−ω2whenω3=1Nowα5=−ω5andβ5=−(ω2)5=−ω3.w2=−ω2=−ω3ω3ω3ω=−ω∴α5+β5=−ω2−ω=−(ω2+ω)=−(−1)=1∴OptionB(Ans)
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
