Advanced MathEasyWhy a square cannot be negative
Advanced Math practice question
A student claims that the equation x² = −4 has a real solution. Which statement explains why the student is wrong?
- A. The square of any real number is never negative.Correct
- B. x² = −4 has two real solutions, not one.
- C. (−2)² = −4, so the solution is not real.
- D. The equation has exactly one real solution, x = −2.
Answer: A. The square of any real number is never negative.
A real number times itself is 0 or positive, so nothing squares to −4.
Why the other answers are wrong
- B. x² = −4 has two real solutions, not one.
- It has no real solutions at all.
- C. (−2)² = −4, so the solution is not real.
- (−2)² = 4, not −4.
- D. The equation has exactly one real solution, x = −2.
- (−2)² = 4, so −2 is not a solution.
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