Question

What are the solutions (including imaginary numbers) to the equation x ²−16=0?

A) x=4, =−4x=−4
B) x=4i, =−4x=−4i
C) x=4, =−4x=−4i
D) x=4i, =−4x=−4

Answer 1

The equation x² − 16 = 0 has two real solutions, x = 4 and x = -4, after factoring it into (x + 4)(x - 4) = 0. There are no imaginary solutions for this particular equation since the solutions are real numbers.

Step-by-step explanation:

The solutions to the equation x² − 16 = 0 can be found by factoring the equation or by completing the square. This quadratic equation can be factored since 16 is a perfect square. The factored form of the equation is (x + 4)(x - 4) = 0. We can find the solutions by setting each factor equal to zero and solving for x.

The first factor gives us the equation x + 4 = 0, which has the solution x = -4. The second factor gives us x - 4 = 0, which has the solution x = 4. Therefore, the solutions to the equation x² − 16 = 0 are x = 4 and x = -4, and there are no imaginary solutions because we have real number solutions.