Find the exact solutions to the quadratic equation in the complex numbers.
-$$x ^ { 2 } + x + 6 = 0$$
A) $\frac { - 1 \pm i \sqrt { 23 } } { 2 }$
B) $\frac { 1 \pm i \sqrt { 23 } } { 2 }$
C) $\frac { 1 \pm \sqrt { 23 } } { 2 }$
D) $\frac { - 1 \pm \sqrt { 23 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 + x + 6 = 0$, we use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = 1$, and $c = 6$. Plugging these values in, we get $x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot 6}}{2 \cdot 1} = \frac{-1 \pm \sqrt{1 - 24}}{2} = \frac{-1 \pm \sqrt{-23}}{2} = \frac{-1 \pm i\sqrt{23}}{2}$.

Find the Exact Solutions to the Quadratic Equation in the Complex