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GMAT Prep : Line & Slope

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GMAT Prep : Line & Slope

by Skywalker » Sat Oct 02, 2010 2:42 am
In the xy plane at what 2 points does the graph y = ( x+a) (x+b) intersect the x axis ?

1) a+b = -1
2) The graph intersects the y axis at (0,-6)

[spoiler]OA = C[/spoiler]

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How do I solve this ?
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by Rahul@gurome » Sat Oct 02, 2010 3:33 am
(1) y = (x+a) (x+b) intersect the x axis so y = 0 implies (x + a)(x + b) = 0 or x^2 +(a + b)x + ab = 0 or x^2 - x + ab = 0, using which we cannot find the values of x.
So, (1) is NOT SUFFICIENT.

(2) y = (x+a) (x+b) intersects the y axis at (0,-6) implies -6 = ab, which again is NOT SUFFICIENT to answer the question.

Combining (1) and (2), x^2 - x - 6 = 0 or (x - 6)(x + 1) = 0, which implies x = -1, 6
Therefore, (-1, 0) and (6, 0) are the two points at which the graph y = ( x+a) (x+b) intersect the x axis.

The correct answer is [spoiler](C)[/spoiler].
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