Solve the equation.
-$\mathrm { m } ^ { 2 } + \mathrm { m } + 4 = 0$
A) $\frac { - 1 - \sqrt { 15 } } { 2 } , \frac { - 1 + \sqrt { 15 } } { 2 }$
B) $\frac { - 1 - \mathrm { i } \sqrt { 15 } } { 2 } , \frac { - 1 + \mathrm { i } \sqrt { 15 } } { 2 }$
C) $\frac { 1 - \sqrt { 15 } } { 2 } , \frac { 1 + \sqrt { 15 } } { 2 }$
D) $\frac { 1 - \mathrm { i } \sqrt { 15 } } { 2 } , \frac { 1 + \mathrm { i } \sqrt { 15 } } { 2 }$

Question

Quizplus · Accepted Answer

The equation $m^2 + m + 4 = 0$ has a discriminant $\Delta = b^2 - 4ac = 1^2 - 4(1)(4) = 1 - 16 = -15$, which is negative, indicating that the roots are complex. Using the quadratic formula, $m = \frac{-b \pm \sqrt{\Delta}}{2a}$, we find the roots to be $\frac{-1 \pm \sqrt{-15}}{2}$, which simplifies to $\frac{-1 \pm i\sqrt{15}}{2}$.

Solve the Equation m2+m+4=0\mathrm { m } ^ { 2 } + \mathrm { m } + 4 = 0m2+m+4=0

Solve the Equation $\mathrm { m } ^ { 2 } + \mathrm { m } + 4 = 0$