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# Is a + b = 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 54436
Is a + b = 0?  [#permalink]

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16 Jul 2017, 23:14
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Difficulty:

65% (hard)

Question Stats:

53% (02:14) correct 47% (03:29) wrong based on 28 sessions

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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.

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Re: Is a + b = 0?  [#permalink]

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16 Jul 2017, 23:41
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
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Re: Is a + b = 0?   [#permalink] 16 Jul 2017, 23:41
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