Question

Given 2x^2 = -8, what are the possible values of x?

A) -2
B) 2
C) 2i or -2i
D) 4i or -4i

Answer 1

The possible values of x given the equation 2x^2 = -8 are 2i and -2i, since the square root of a negative number involves the imaginary unit i.

Step-by-step explanation:

To find the possible values of x given the equation 2x^2 = -8, we must first divide both sides by 2 to simplify the equation to x^2 = -4. Since the square of a real number cannot be negative, we resort to imaginary numbers to solve this. We find that x must be either √-4 or -√-4, which can be expressed in terms of i, the imaginary unit where i^2 = -1. Thus, the possible values of x are 2i and -2i, since √-4 = 2i and -√-4 = -2i.