Question

solution sets of quadratic equations practice
complete this assessment to review what youve learned. it will not count toward your grade.
how many solutions would the equation $x^2 = -9$ have? you do not need to solve for $x$. (1 point)
the equation would have \square solution(s).

Explanation:

Step1: Recall the property of real numbers

For any real number \( x \), the square of \( x \) (i.e., \( x^2 \)) is always non - negative. That is, if \( x\in\mathbb{R} \), then \( x^{2}\geq0 \).

Step2: Analyze the given equation

The given equation is \( x^{2}=- 9 \). But we know that the left - hand side \( x^{2} \) (for real \( x \)) is non - negative and the right - hand side \( - 9 \) is negative. So, there is no real number \( x \) that can satisfy the equation \( x^{2}=-9 \) in the set of real numbers. However, if we consider complex numbers, the solutions are \( x = \pm3i \), but the question is likely asking about real solutions (since it's a basic quadratic equation question at this level). So, the number of real solutions is 0.

Answer:

0