Question

find the solutions of the quadratic equation $x^2 + x + 1 = 0$. choose 1 answer: a $\frac{1}{2} pm \frac{sqrt{3}}{2}i$ b $-\frac{1}{2} pm \frac{sqrt{3}}{2}$ c $-\frac{1}{2} pm \frac{sqrt{3}}{2}i$ d $\frac{1}{2} pm \frac{sqrt{3}}{2}$

Explanation:

Step1: Recall quadratic formula

For \(ax^2 + bx + c = 0\), solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Here, \(a = 1\), \(b = 1\), \(c = 1\).

Step2: Calculate discriminant

Discriminant \(D=b^2 - 4ac=(1)^2 - 4(1)(1)=1 - 4=-3\).

Step3: Apply quadratic formula

\(x=\frac{-1\pm\sqrt{-3}}{2}=\frac{-1\pm\sqrt{3}i}{2}=-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i\).

Answer:

C. \(-\frac{1}{2} \pm \frac{\sqrt{3}}{2}i\)