Let's analyze the situation you described: you have an equation where one side is a squared variable expression (let's denote it as \( x^2 \)), and the other side is a numeric expression (let's denote it as \( k \)). The equation can be expressed as:
\[ x^2 = k \]
Now, we will evaluate the scenarios for \( k \):
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If \( k > 0 \):
- In this case, the equation \( x^2 = k \) has two solutions. Specifically, \( x = \sqrt{k} \) and \( x = -\sqrt{k} \). Therefore, there are two solutions.
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If \( k = 0 \):
- The equation \( x^2 = 0 \) has one solution, which is \( x = 0 \).
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If \( k < 0 \):
- The equation \( x^2 = k \) has no real solutions because the square of any real number is non-negative, and therefore cannot equal a negative number.
Given that your question focuses on the scenario where the numeric expression is greater than zero, the correct statement among the options provided is:
A. If the numeric expression is greater than zero there are two solutions.
This is the correct answer.