If a, b are the roots of the equation x2+x+1=0, then a2+b2=
-1
Given equation:x2+x+1=0Also, a and b are the roots of the given equationSum of the roots=a+b=−coefficient of xcoefficientofx2=−11=−1Product of the roots ab=−coefficient termcoefficientofx2=11=1∴(a+b)2=a2+b2+2ab⇒1−2=a2+b2⇒a2+b2=−1