Question

Assuming an equation with one side as a squared variable expression and the other side as a numeric expression which of the following statements is correct?
A. If the numeric expression is greater then zero there are two solutions
B. If the numeric expression is greater then zero there is one solution
C. If the numeric expression is greater then zero there are no solutions

Answer 1

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 \( k \):

1. **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.

2. **If \( k = 0 \)**:
- The equation \( x^2 = 0 \) has one solution, which is \( x = 0 \).

3. **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.