Question

What is the solution of the equation x^2 + 4x + 10 = 0?

Answer 1

`x=-2\pm i\sqrt[]{6}`

1) Let's solve this quadratic equation by the Quadratic Formula Method.

2) So, we can write out the following:

`\begin{gathered} x^2+4x+10=0 \\ x=\frac{-b\pm\sqrt[]{\Delta}}{2a} \\ x_{}=(-4\pm√(4^2-4\cdot\:1\cdot\:10))/(2\cdot\:1) \\ x_1=(-4+2√(6)i)/(2)\Rightarrow\quad x_1=-2+√(6)i \\ x_2=(-4-2√(6)i)/(2)\Rightarrow\quad x_2=-2-\sqrt[]{6}i \end{gathered}`

Note that as the Discriminant is negative, then this quadratic yields two complex roots. Adjusting to the way the options are presented, we can state the answer is:

`\quad x=-2\pm i\sqrt[]{6}`