Solution Sets of Quadratic Equations Practice

Question

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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).
Remaining Attempts : 3
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Answer 1

To determine how many solutions the equation \( x^2 = -9 \) has, we need to analyze the equation.

Since the left side, \( x^2 \), represents the square of a real number, it is always non-negative (0 or positive). The right side of the equation, \(-9\), is negative.

In the real number system, there are no real numbers whose square is negative. Therefore, this equation does not have any real solutions.

However, if we consider complex numbers, we can solve this equation as follows: \[ x^2 = -9 \implies x = \pm 3i \] In this case, there are two complex solutions.

In summary, the equation \( x^2 = -9 \) has:

• 0 real solutions
• 2 complex solutions

Since the question asks how many solutions there are without needing to specify the type, you can say:

The equation would have 0 solutions (considering only real solutions).