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If a^2 + 7a < 0, then which one of the following could be the value of

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If a^2 + 7a < 0, then which one of the following could be the value of  [#permalink]

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New post 08 Mar 2017, 05:11
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If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3
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Re: If a^2 + 7a < 0, then which one of the following could be the value of  [#permalink]

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New post 08 Mar 2017, 08:34
vikasp99 wrote:
If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3


\(a^2 + 7a < 0\)

\(= a ( a + 7 ) < 0\)

So, \(a < 0\) and \(a < -7\)

Among the given options and considering the form \(a < -7\) , only option (A) –3 is true...
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Re: If a^2 + 7a < 0, then which one of the following could be the value of  [#permalink]

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New post 10 Mar 2017, 10:33
vikasp99 wrote:
If a^2 + 7a < 0, then which one of the following could be the value of a?

(A) –3

(B) 0

(C) 1

(D) 2

(E) 3


We can substitute our answer choices for a:

A) -3

Is (-3)^2 + 7(-3) < 0 ?

Is 9 - 21 < 0 ?

Since the answer is YES, answer choice A is correct.

Alternate Solution:

The expression a^2 + 7a can only be negative if 7a is negative (because the square of every real number is nonnegative). If 7a is negative, a must be negative, and there is only one answer choice that is negative, which is -3.

Answer: A
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Re: If a^2 + 7a < 0, then which one of the following could be the value of &nbs [#permalink] 10 Mar 2017, 10:33
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