Solve the equation using the quadratic formula.
-$$x ^ { 2 } + x + 4 = 0$$
A) $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$
B) $\left\{ \frac { - 1 \pm \sqrt { 15 } } { 2 } \right\}$
C) $\left\{ \frac { 1 \pm \sqrt { 15 } } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 15 } } { 2 } \mathrm { i } \right\}$

Question

Quizplus · Accepted Answer

The quadratic formula is $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = 1$, and $c = 4$. Plugging these values in, we get $\frac{-1 \pm \sqrt{1^2 - 4(1)(4)}}{2(1)} = \frac{-1 \pm \sqrt{1 - 16}}{2} = \frac{-1 \pm \sqrt{-15}}{2}$. Since the square root of a negative number involves $i$, the correct answer is $\frac{-1}{2} \pm \frac{\sqrt{15}}{2}i$, which matches choice D.

Solve the Equation Using the Quadratic Formula x2+x+4=0x ^ { 2 } + x + 4 = 0x2+x+4=0

Solve the Equation Using the Quadratic Formula $x ^ { 2 } + x + 4 = 0$