Solve the following quadratics $ x^{2}+x+1 = 0 $
- $\dfrac{1}{2}\pm \dfrac{i\sqrt{3}}{2} $
- $-\dfrac{1}{2}\pm \dfrac{i}{2} $
- $-\dfrac{1}{2}\pm \dfrac{i\sqrt{3}}{2} $
- $\dfrac{1}{2}\pm \dfrac{i}{2} $
Reveal answer
Fill a bubble to check yourself
C
Correct answer
Explanation
Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a, for x^2 + x + 1 = 0, we get x = (-1 +/- sqrt(1 - 4)) / 2 = (-1 +/- sqrt(-3)) / 2 = -1/2 +/- i*sqrt(3)/2.
AI explanation
Using the quadratic formula x = (-b plus or minus sqrt(b^2 - 4ac)) / 2a, we substitute a = 1, b = 1, and c = 1. The discriminant is 1^2 - 4(1)(1) = -3, meaning the roots are (-1 plus or minus i*sqrt(3)) / 2. This result is written as -1/2 plus or minus (i*sqrt(3))/2.