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07 Dec 2021, 09:15
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
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Question Stats:
54% (02:39) correct
46%
(02:21)
wrong
based on 140
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If the roots of the equation \((x + 1)(x + 9) + 8 = 0\) are a and b, then the roots of the equation \((x + a)(x + b) - 8 = 0\) are
A. 1 and 9
B. -4 and -6
C. 4 and 6
D. -1 and -9
E. -1 and 9
Are You Up For the Challenge: 700 Level Questions
A. 1 and 9
B. -4 and -6
C. 4 and 6
D. -1 and -9
E. -1 and 9
Are You Up For the Challenge: 700 Level Questions
07 Dec 2021, 09:27
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Given x^2 + 10x + 17 = 0
=> a + b = -10
and ab = 17
Now We have to find roots of (x + a)(x + b) - 8 = 0
Let k and m be the roots of this equation
Hence k + m = -(a + b) and km = ab - 8
=> k + m = 10 and km = 17 - 8 = 9
substituting k + 9/k = 10
=> (k - 1)(k - 9) = 0
=> k = 1, 9
If k = 1 them m = 9 and
If k = 9 them m = 1
Hence Option A
=> a + b = -10
and ab = 17
Now We have to find roots of (x + a)(x + b) - 8 = 0
Let k and m be the roots of this equation
Hence k + m = -(a + b) and km = ab - 8
=> k + m = 10 and km = 17 - 8 = 9
substituting k + 9/k = 10
=> (k - 1)(k - 9) = 0
=> k = 1, 9
If k = 1 them m = 9 and
If k = 9 them m = 1
Hence Option A
02 Feb 2025, 04:31
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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