If ɑ,β are the roots of the equation x2-x+1=0 then ɑ2009+β2009=
-1
1
-2
2
Explanation for the correct option:
Step 1. Find the value of ɑ2009+β2009:
As we know,
x3+1=(x+1)(x2–x+1)=0
⇒ x3=–1
Step 2. ɑ,β are the roots of the equation x2-x+1=0, then
(ɑ+β)=1,(ɑβ)=1
∵x3+1=0
⇒ɑ3=–1,β3=–1
∴ɑ2009+β2009=ɑ2010ɑ+β2010β=(ɑ3)670ɑ+β3670β=1ɑ+1β=α+βαβ=11=1
Hence, Option ‘B’ is Correct.