Midpoint Summative Practice Exam

Which statement is true for all real numbers x about x^2?

It is always negative It is nonnegative It is always positive It is undefined

Correct Answer:

It is nonnegative

Explanation:

Squaring a real number always gives a nonnegative result. Since x^2 = x·x, the product of a number with itself is positive if x ≠ 0 and zero if x = 0, never negative. So for every real x, x^2 ≥ 0. That’s why the statement “x^2 is nonnegative” is true for all real numbers. It isn’t always negative, since it can be zero; it isn’t always positive, since zero is possible; and it isn’t undefined, since the operation is defined for every real x.

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