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For integers a and x
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16 Feb 2021, 05:18
16 Feb 2021, 05:18
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47% (01:23) correct
52% (01:09) wrong based on 87 sessions
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For integers \(a\) and \(x\), which of the following values of \(a\) guarantees that \(4x^2 + ax + 16\) is a perfect square?
A. −16
B. −4
C. 4
D. 8
E. 12
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. −16
B. −4
C. 4
D. 8
E. 12
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
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Re: For integers a and x
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16 Feb 2021, 07:03
16 Feb 2021, 07:03
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Carcass wrote:
For integers \(a\) and \(x\), which of the following values of \(a\) guarantees that \(4x^2 + ax + 16\) is a perfect square?
A. −16
B. −4
C. 4
D. 8
E. 12
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. −16
B. −4
C. 4
D. 8
E. 12
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Given: 4x² + ax + 16
(2x)² = 4x²
4² = 16
So, it appears that EITHER 4x² + ax + 16 = (2x + 4)² OR 4x² + ax + 16 = (2x - 4)²
Now check each case:
Expand (2x + 4)² to get: 4x² + 16x + 16
Here, a = 16, but 16 is not one of the answer choices
Expand (2x - 4)² to get: 4x² - 16x + 16
Here, a = -16
Answer: A
Re: For integers a and x
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19 Apr 2022, 12:10
19 Apr 2022, 12:10
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