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16 Jul 2017, 23:14
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:34) correct
46%
(02:21)
wrong
based on 63
sessions
History
Date
Time
Result
Not Attempted Yet
Is a + b = 0?
(1) The roots of the equation \(\frac{a}{(x − a)} + \frac{b}{(x − b)} = 1\), where a and b are constants and x is a variable, are equal in magnitude, but opposite in sign.
(2) The equation \(x(x − a) + x (x − b) = 0\), where a and b are constants and x is a variable, has equal roots.
(1) The roots of the equation \(\frac{a}{(x − a)} + \frac{b}{(x − b)} = 1\), where a and b are constants and x is a variable, are equal in magnitude, but opposite in sign.
(2) The equation \(x(x − a) + x (x − b) = 0\), where a and b are constants and x is a variable, has equal roots.
16 Jul 2017, 23:41
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As attached in the picture.
Each statement alone is sufficient to answer the question. So answer is D.
We need to know that for a quadratic equation: ax^2 + bx + c = 0, sum of roots = -b/a and product of roots = c/a
Each statement alone is sufficient to answer the question. So answer is D.
We need to know that for a quadratic equation: ax^2 + bx + c = 0, sum of roots = -b/a and product of roots = c/a
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14 Feb 2020, 01:07
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Bunuel
Solution
Step 1: Analyse Question Stem
We don’t know anything about \(a\) and \(b\).
We need to find; is \(a+b = 0\)?
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1:
- • \(\frac{a}{(x-a)} + \frac{b}{(x-b)}=1\)
- • \(a*(x-b) + b*(x-a)=(x-a)*(x-b)\)
• \(a*x -a*b+b*x-a*b= x^2 -b*x -a*x +a*b\)
• \(x^2 +2*(a+b)*x – 3*a*b=0\)
- o Now, this is a quadratic equation, it means it will have only two roots.
- o Sum of the roots = 0…(i)
- o Equate this result to equation (i), we get
- \(-2*(a+b)=0\)
\(a+ b = 0\)
Statement 2:
- • \(x*(x-a)+x*(x-b)=0\)
- • \(x*(x-a+x-b)=0\)
• \(x*(2x-a-b)=0\)
- Thus,\( x = \)0, and \(x=\frac{(a+b)}{2}\)
- o It is given that above equation has equal roots,
- • \(a + b = 0\).
