Hello,

The roots of the equation ax^2 + bx + c = 0 is given by the formula:

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

Now for equation x^2 + x + 1, we have:

a = 1

b = 1

c = 1

Substituting the value in the above equation, we get:

x = [-1 + sqrt( 1^2 - 4*1*1)] / (2*1) or x = [-1 - sqrt( 1^2 - 4*1*1)] / (2*1)

x = [-1 + sqrt(-3)]/2 or x = [-1 - sqrt(-3)]/2

x = [-1 + sqrt(3)*i]/2 or x = [-1 - sqrt(3)*i]/2 (Answer) [ Because i^2 = -1]