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Chapter 7: Problem 2

If \(x<0\), which of the following is true? \(O x^2\) is positive. \(x^2\) is negative. \(x^2\) could be either positive or negative. I don't know.

Short Answer

Expert verified
The statement ' \(x^2\) is positive' is correct when \(x<0\).

Step by step solution

01

Understand the property of squaring

Consider the key property of squaring: Any real number, when squared, becomes a positive number. This is because a negative number times a negative number equals a positive number.
02

Apply the property to our case

Given that \(x\) is less than zero, it means x is a negative number. When we square \(x\) (or \(x^2\)), we multiply \(x\) by itself. Since a negative number times a negative number yields a positive number, \(x^2\) will always be positive.
03

Analyze the options

Now, we examine the provided statements. The first one \(x^2\) is positive, aligns with our solution. The remaining options suggest that \(x^2\) could be negative or has an uncertain value. From our understanding of the squaring operation, we know that these options are not valid.

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