Question

In the complex number system, find the complex solutions of the equation$x^2+2x+2=0$

Short answer

The roots of the polynomial is$-1+i,-1-i$

Step-by-step solution

Given information

We are given a polynomial$x^2+2x+2=0$

Solve using quadratic formula

We have,

$x^2+2x+2=0$

hence,

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ x=\frac{-2\pm \sqrt{4-8}}{2} \\ x=\frac{-2\pm 2i}{2} \\ x=-1\pm i \end{gathered}$$

Conclusion

The roots of the polynomial is$-1+i,-1-i$