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Fallacy

If a and x re...

Question

If a and x represent real numbers for which $x^{2} = - a$ , which of the following statements could be true?
I. $a > 0$
II. $a = 0$
III. $a < 0$

None

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II only

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III only

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I and II only

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II and III only

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Solution

The correct option is E II and III only
Given $x^{2} = - a$ , we know that square of something is always non negative.
Therefore $- a$ is always non negative. which implies $a$ can be $0$ or negative.
Therefore the correct answer is option $E$ .

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If a and x represent real numbers for which x2=−a, which of the following statements could be true?I. a>0II. a=0III. a<0

The correct option is E II and III onlyGiven x2=−a, we know that square of something is always non negative.Therefore −a is always non negative. which implies a can be 0 or negative.Therefore the correct answer is option E.

If a and x represent real numbers for which $x^{2} = - a$ , which of the following statements could be true?
I. $a > 0$
II. $a = 0$
III. $a < 0$

The correct option is E II and III only
Given $x^{2} = - a$ , we know that square of something is always non negative.
Therefore $- a$ is always non negative. which implies $a$ can be $0$ or negative.
Therefore the correct answer is option $E$ .