Solve the equation.
-$$\mathrm { n } ^ { 2 } + \mathrm { n } + 7 = 0$$
A) $\left\{ \frac { - 1 - 3 \sqrt { 3 } } { 2 } , \frac { - 1 + 3 \sqrt { 3 } } { 2 } \right\}$
B) $\left\{ \frac { - 1 - 3 i \sqrt { 3 } } { 2 } , \frac { - 1 + 3 i \sqrt { 3 } } { 2 } \right\}$
C) $\left\{ \frac { 1 - 3 \sqrt { 3 } } { 2 } , \frac { 1 + 3 \sqrt { 3 } } { 2 } \right\}$
D) $\left\{ \frac { 1 - 3 \mathrm { i } \sqrt { 3 } } { 2 } , \frac { 1 + 3 \mathrm { i } \sqrt { 3 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

The equation $n^2 + n + 7 = 0$ has no real solutions because the discriminant $b^2 - 4ac = 1^2 - 4(1)(7) = 1 - 28 = -27$ is negative. Using the quadratic formula, $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, we find the solutions to be $n = \frac{-1 \pm \sqrt{-27}}{2}$, which simplifies to $n = \frac{-1 \pm 3i\sqrt{3}}{2}$, matching choice B.

Solve the Equation n2+n+7=0\mathrm { n } ^ { 2 } + \mathrm { n } + 7 = 0n2+n+7=0

Solve the Equation $\mathrm { n } ^ { 2 } + \mathrm { n } + 7 = 0$