Question

If a and b are roots of the equation x^2+x+1=0 , then the value of a^2+b^2 is ? ​

Answer 1

Answer:

Step-by-step explanation:

x^2+x+1=0

using determinant for to find the roots

(-b±√(b²-4ac))/2a

a=1, b=1, c=1

(-1±√(1-4))/2

-1/2 + (i√3)/2 , -1/2 - (i√3)/2

now

(-1/2 + i√3/2)² + (-1/2 - i√3/2)²

= 1/4 + i²3/4 - i√3 + 1/4 + i²3/4 + i√3

= 2/4 -3/4 - 3/4

= 2/4 - 6/4

= -4/4

= -1