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x^2 − 11x + |p| = 0, where x is a variable and p is a constant, has 2
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24 Sep 2021, 10:51
24 Sep 2021, 10:51
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Question Stats:
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52% (02:22) wrong based on 94 sessions
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\(x^2 − 11x + |p| = 0\), where \(x\) is a variable and \(p\) is a constant, has 2 distinct integer roots.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of integer values that \(p\) can take |
10 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
x^2 − 11x + |p| = 0, where x is a variable and p is a constant, has 2
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24 Sep 2021, 13:55
24 Sep 2021, 13:55
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very typical of the discriminant case problem
\(\sqrt{11^2-4*|p|}>0\) and the discriminant actually must be odd integer for x to have integer roots
there are not many perfect squares after the multiples of 4 are subtracted; one is \(9^2\) and \(|p|=8\)
another is \(7^2\) and \(|p|=18\)
yet, another is \(5^2\) and \(|p|=24\)
...
summing up, all perfect squares of odd numbers below 11 and including 11, i.e. 11, 9, 7, 5, 3, 1 are suitable here
p={-30, -28, -24, -18, -8, 0, 8, 18, 24, 28, 30} set contains 11 integers
answer is A, as Quantity A=11 > Quantity B=10
\(\sqrt{11^2-4*|p|}>0\) and the discriminant actually must be odd integer for x to have integer roots
there are not many perfect squares after the multiples of 4 are subtracted; one is \(9^2\) and \(|p|=8\)
another is \(7^2\) and \(|p|=18\)
yet, another is \(5^2\) and \(|p|=24\)
...
summing up, all perfect squares of odd numbers below 11 and including 11, i.e. 11, 9, 7, 5, 3, 1 are suitable here
p={-30, -28, -24, -18, -8, 0, 8, 18, 24, 28, 30} set contains 11 integers
answer is A, as Quantity A=11 > Quantity B=10
KarunMendiratta wrote:
\(x^2 − 11x + |p| = 0\), where \(x\) is a variable and \(p\) is a constant, has 2 distinct integer roots.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of integer values that \(p\) can take |
10 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
General Discussion
Re: x^2 11x + |p| = 0, where x is a variable and p is a constant, has 2
[#permalink]
22 Aug 2022, 12:44
22 Aug 2022, 12:44
Is there some other solution?
