Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .
A) -256
B) $\pm 256 i$
C) $\pm 16$
D) $\pm 16 i$
E) $16 i$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 + 256 = 0$, we can rearrange it to $x^2 = -256$. Taking the square root of both sides gives $x = \pm \sqrt{-256}$. Since the square root of a negative number involves the imaginary unit $i$, where $i^2 = -1$, we get $x = \pm \sqrt{256}i$, which simplifies to $x = \pm 16i$.

Find All Real and Complex Solutions of the Quadratic Equation x2+256=0x ^ { 2 } + 256 = 0x2+256=0

Find All Real and Complex Solutions of the Quadratic Equation $x ^ { 2 } + 256 = 0$