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Problem from mba.com practice test 1

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Problem from mba.com practice test 1

by ksutthi » Sat Jul 05, 2008 3:24 am
Can anyone help me solve this question? I don't seem to be able to derive the answer.

In the xy-plane, at what two 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)

Many thanks.
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Source: — Data Sufficiency |
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by ed09 » Sat Jul 05, 2008 9:23 pm
I dare to say that the answer is C.

Rewrite the equation in form of quadratic
y=x^2+(a+b)x+ab

0=x^2+(a+b)x+ab - real solutions of this equation are x-coordinates of points where the graph intersects the x-axis.

(1)
a+b=-1 => x^2-x+ab=0
a+b=-1 - does not give enough data to be sure about ab
INSUFFICIENT

(2) (0,6) - this is one root
0=x^2+(a+b)x+ab; (x-6)(x+z)=0; x2+zx-6x-6z=0; x2+(z-6)x-6z=0
there is no enough information to solve this equation further
INSUFFICIENT

(3) COMBINE
from (2) x2+(z-6)x-6z=0
from (1) 0=x^2+(a+b)x+ab; a+b=-1
=>(a+b)=z-6=-1 => z=5 => -6z=-30
hence the equation sought is x2-x-30=0 or (x-6)(x+5)=0
thus, roots of (0,6) and (0,-5) are coordinates of points where the graph intersects the x-axis.
SUFFICIENT

I'll be appreciate someone who point out a mistake in my solution or show a shorter/simpler way.

Best!
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