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07 May 2020, 10:22
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
10% (01:29) correct
90%
(01:32)
wrong
based on 48
sessions
History
Date
Time
Result
Not Attempted Yet
a = ?
(1) a^3 + a^2 + 2a = 0
(2) a = -2a
OA
(1) a^3 + a^2 + 2a = 0
(2) a = -2a
@MathsRevolution
your question where we must find a =?
you mention that a(a^2 + a + 2) = 0 because it's "positive"
I'm not quite sure I understand this
according to the discriminant there are no solutions, not even 0, so why would a= 0?
i also put the above equation into a quadratic solver and it gives me 2 complex roots, so therefore it has 2 solutions??
can you advise? thanks
your question where we must find a =?
you mention that a(a^2 + a + 2) = 0 because it's "positive"
I'm not quite sure I understand this
according to the discriminant there are no solutions, not even 0, so why would a= 0?
i also put the above equation into a quadratic solver and it gives me 2 complex roots, so therefore it has 2 solutions??
can you advise? thanks
OA
07 May 2020, 10:25
Kudos
Bookmarks
your question where we must find a =?
you mention that a(a^2 + a + 2) = 0 because it's "positive"
I'm not quite sure I understand this
according to the discriminant there are no solutions, not even 0, so why would a= 0?
i also put the above equation into a quadratic solver and it gives me 2 complex roots, so therefore it has 2 solutions??
can you advise? thanks
you mention that a(a^2 + a + 2) = 0 because it's "positive"
I'm not quite sure I understand this
according to the discriminant there are no solutions, not even 0, so why would a= 0?
i also put the above equation into a quadratic solver and it gives me 2 complex roots, so therefore it has 2 solutions??
can you advise? thanks
07 May 2020, 21:19
Kudos
Bookmarks
mrcentauri
We need to determine the value of \(a \)
Though not mentioned, \(a\) must be real (complex numbers are beyond the score of GMAT)
From Statement 1: \(a^3 + a^2 + 2a = 0\)
=> \(a(a^2 + a + 2) = 0\)
=> a = 0 or a^2 + a + 2 = 0
However: a^2 + a + 2 = a^2 + 2(a)(1/2) + (1/2)^2 + 7/4 = (a + 1/2)^2 + 7/4
Thus, (a^2 + a + 2) is 7/4 more than a perfect square => it cannot be zero
=> a = 0 (Sufficient)
From statement 2:
a = -2a
=> a + 2a = 0
=> 3a = 0
=> a = 0 (sufficient)
Thus, either statement alone is sufficient
Answer D
