Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

A) -256
B) $±256i\pm 256 i$
C) $±16\pm 16$
D) $±16i\pm 16 i$
E) $16 i$

Question

Find all real and complex solutions of the quadratic equation

x ^ { 2 } + 256 = 0

.

A) -256
B)

±256i\pm 256 i

C)

±16\pm 16

D)

±16i\pm 16 i

E)

16 i

Megan Stretton · Accepted Answer

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

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

A) -256
B) $±256i\pm 256 i$
C) $±16\pm 16$
D) $±16i\pm 16 i$
E) $16 i$

Definitions

Learning Objectives

Learning Objectives

Related questions

Find all real and complex solutions of the quadratic equation x2+256=0x ^ { 2 } + 256 = 0x2+256=0 .A) -256B) ±256i\pm 256 i±256i C) ±16\pm 16±16 D) ±16i\pm 16 i±16i E) 16i16 i16i

Definitions

Learning Objectives

Learning Objectives

Related questions

Find all real and complex solutions of the quadratic equation $x ^ { 2 } + 256 = 0$ .

A) -256
B) $±256i\pm 256 i$
C) $±16\pm 16$
D) $±16i\pm 16 i$
E) $16 i$