Imaginary Root Verification...?

Question

Alright, so we all know that when the discriminant is negative in the quadratic formula, negative roots are generated...
For a function f(x) = x^2 + x +1... are the imaginary roots

-0.5 + 0.866025i
-0.5 - 0.866025i

??

Please check up to verify my solution. Thank you all.

Answer 1

Find the roots.

x² + x + 1 = 0

x = [-1 ± √(1² - 4*1*1)] / (2*1) = [-1 ± √(-3)] / 2

x = (-1 ± i√3) / 2

Your roots are correct.