UPSC NDA Math Model Paper 1

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