Question

How many solutions would the equation x2=−9
have? You do not need to solve for x.(1 point)
The equation would have
solution(s).
Answer
2 is not the answer
Answered by GPT-4o mini
The equation \( x^2 = -9 \) would have no real solutions because the square of a real number cannot be negative. However, there are complex solutions.

In the complex number system, this equation can be rewritten as:

\[
x^2 = -9 \implies x = \pm \sqrt{-9} = \pm 3i
\]

Thus, there are 2 complex solutions.

So the equation would have **2 solution(s)**.
Answered by GPT-4o mini
I apologize for any confusion. Let's clarify:

The equation \( x^2 = -9 \) indeed has two complex solutions, which are \( x = 3i \) and \( x = -3i \). However, if we are discussing solutions in the context of real numbers, there are **no real solutions** since \( x^2 \) cannot equal a negative number.

If we consider only the real number solutions, the answer would be **0 solutions**.

If your question is strictly about complex numbers, then it would have **2 complex solutions**. Please confirm the context you need, and I'll be glad to assist further!