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GMAT PREP (XY PLANE)

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GMAT PREP (XY PLANE)

by relaxin99 » Mon Feb 16, 2009 4:29 pm
In the xy-plane, at what points does the graph of y = (x + a)(x + b) intersect the x-axis?

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



Can someone please explain their answer as well, the correct answer is down below
























The answer is C
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Source: — Data Sufficiency |
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by tini » Mon Feb 16, 2009 6:07 pm
y=(x+a)(x+b)
when intersects at y,
-6=ab..eqn 1

given that a+b=1..eqn 2
solve 1 & 2
we get b=3,a=-4 and b=-2 and a=3

when intersect at x,
y will be 0

0=(x+a)(x+b)
x = -a,-b

point is (-a,0) or (-b,0)

-6=3.(-2)
b=3,a=-2

x=2,-3

both info is reqd to solve
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by sanju09 » Wed Feb 18, 2009 5:15 am
Take x^2 + (a + b) x + a b = 0 ready, to get to know the points where it intersects the x-axis.

(1) reduces the equation to x^2 + x + a b = 0. With a b not known, this alone is insufficient.

(2) helps us take a b = -6 and reduces the equation to x^2 + (a + b) x - 6. With a + b not known, this alone is insufficient.

Merger makes us have x^2 + x - 6 = 0, whose discriminant (1)^2 - 4 (1) (-6) = 25 > 0, so real, rational and different roots are also guaranteed. Now C surely is the right answer.
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