The given equation is x2+x+1=0 Comparing with standard form we get a=1,b=1,c=1. It is given that α and β are the roots. Therefore, using the definition we can write: α+β=−1 and αβ=1 We will calculate the required value as follows: α2+β2=(α+β)2−2αβ=(−1)2−2(1)=1−2=−1 Therefore, α2+β2=−1