Find the nonreal complex solutions of the equation.
-$-5 x^{2}-4 x-4=0$
A) $\left\{\frac{2}{5},-\frac{6}{5}\right\}$

B) $\left\{\frac{-4+\mathrm{i} \sqrt{64}}{10}, \frac{-4-\mathrm{i} \sqrt{64}}{10}\right\}$

C) $\left\{\frac{-2+4 \mathrm{i}}{5}, \frac{-2-4 \mathrm{i}}{5}\right\}$

D) $\left\{\frac{2+4 \mathrm{i}}{5}, \frac{2-4 \mathrm{i}}{5}\right\}$

Question

Find the nonreal complex solutions of the equation.
-$-5 x^{2}-4 x-4=0$
A) $\left\{\frac{2}{5},-\frac{6}{5}\right\}$

B) $\left\{\frac{-4+\mathrm{i} \sqrt{64}}{10}, \frac{-4-\mathrm{i} \sqrt{64}}{10}\right\}$

C) $\left\{\frac{-2+4 \mathrm{i}}{5}, \frac{-2-4 \mathrm{i}}{5}\right\}$

D) $\left\{\frac{2+4 \mathrm{i}}{5}, \frac{2-4 \mathrm{i}}{5}\right\}$

Quizplus · Accepted Answer

To find the nonreal complex solutions, we use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ with $a = -5$, $b = -4$, and $c = -4$. Plugging these values in, we get: $$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(-5)(-4)}}{2(-5)} = \frac{4 \pm \sqrt{16 - 80}}{-10} = \frac{4 \pm \sqrt{-64}}{-10}$$ Simplifying further, we get: $$x = \frac{4 \pm 8i}{-10} = \frac{-2 \pm 4i}{5}$$ Thus, the nonreal complex solutions are $\frac{-2+4i}{5}$ and $\frac{-2-4i}{5}$, which matches option C.

Find the Nonreal Complex Solutions of the Equation −5x2−4x−4=0-5 x^{2}-4 x-4=0−5x2−4x−4=0

Find the Nonreal Complex Solutions of the Equation $-5 x^{2}-4 x-4=0$