Question

essay 20 points
solve using the quadratic formula:
2m² + 4m + 5 = 0
*must show your work to earn credit

Explanation:

Step1: Identify coefficients

For the quadratic equation $2m^{2}+4m + 5=0$, we have $a = 2$, $b = 4$, $c = 5$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(4)^{2}-4\times2\times5=16 - 40=- 24$.

Step3: Apply quadratic formula

The quadratic formula is $m=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute $a = 2$, $b = 4$, $\Delta=-24$:
\[

$$\begin{align*} m&=\frac{-4\pm\sqrt{-24}}{2\times2}\\ &=\frac{-4\pm\sqrt{24}\times\sqrt{-1}}{4}\\ &=\frac{-4\pm2\sqrt{6}i}{4}\\ &=\frac{-2\pm\sqrt{6}i}{2} \end{align*}$$

\]

Answer:

$m=\frac{-2 + \sqrt{6}i}{2}$ and $m=\frac{-2-\sqrt{6}i}{2}$