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19 Mar 2020, 08:12
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Difficulty:
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Question Stats:
80% (01:11) correct
20%
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wrong
based on 112
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Which of the following could equal zero for some value of x?
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 514
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Products:
19 Mar 2020, 08:22
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Bunuel
Which of the following could equal zero for some value of x?
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
I. \(3x^2 − 12\); x = 2
III. \(x^2 + 7x + 6\); x = -6,-1
II. \(x^2 + x^4 + 1\); this can not equate to 0 because first and second term will always be positive.
Ans: D
19 Mar 2020, 08:48
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Bunuel
Which of the following could equal zero for some value of x?
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
I. \(3x^2 − 12\)
II. \(x^2 + x^4 + 1\)
III. \(x^2 + 7x + 6\)
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
I. \(3x^2 − 12 = 0\)
Factor: \(3(x^2 − 4) = 0\)
Factor again: \(3(x+2)(x-2) = 0\)
Solve: \(x = -2\) or \(x = 2\)
So, \(3x^2 − 12\) COULD equal zero
Check the answer choices....eliminate B
II. \(x^2 + x^4 + 1 = 0\)
Subtract \(1\) from both sides to get: II. \(x^2 + x^4 = -1\)
IMPORTANT: Since \(x^2\) and \(x^4\) are greater than or equal to 0 for all values of \(x\), it is IMPOSSIBLE for \(x^2\) and \(x^4\) to have a sum of \(-1\)
So, \(x^2 + x^4 + 1\) can NEVER equal zero
Check the answer choices....eliminate C and E
III. \(x^2 + 7x + 6=0\)
Factor to get: \((x + 1)(x+6)=0\)
Solve: \(x = -1\) or \(x = -6\)
So, \(x^2 + 7x + 6\) COULD equal zero
Check the answer choices....eliminate A
Answer: D
Cheers,
Brent
