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# In the xy plane, at what two points does the graph of

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Manager
Joined: 08 Jan 2007
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In the xy plane, at what two points does the graph of [#permalink]  07 Aug 2007, 02:39
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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)

this is a GMATPrep question
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Director
Joined: 12 Jul 2007
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I'm thinking C for this one.

1. a + b = -1 this could be any two numbers with a sum of -1 now. insufficient

2. The graph intersects the y-axis at (0, -6). so plug 0 in for X in this equation:

y = x^2 + xb + xa + ab

and you're left with y = ab = -6. now this taken on it's own could be any two numbers with -6 as the product (1, -6) or (2, -3) etc. insufficient as well

taken on their own they aren't much help, but when taken together you know that the sum of A and B is -1 and the product is -6. The only two numbers that work now are -3 and 2.

anyone agree with this one?
Senior Manager
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Re: DS intersect [#permalink]  07 Aug 2007, 14:00
VAGMAT wrote:
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)

The question can be understood as: what are a and b? (a and b are the intersects of the function with the x axis).

(1) Insuff.
(2) Same.

(12) a = 0; then b = -1. Suff. C.
VP
Joined: 10 Jun 2007
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Re: DS intersect [#permalink]  07 Aug 2007, 15:00
VAGMAT wrote:
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)

this is a GMATPrep question

Got C too.
From the question, we know that the two values that we need to find are a and b.
(1) -a+b = 1, doesn't tell much. INSUFFICIENT.
(2) plug in x=0, you have -6 = a*b
INSUFFICIENT.

Together, two equations, two unknowns. SUFFICIENT.
Manager
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I am not able to solve for a2-2a+6, which is the equation I get. It gives a complex number. In such a case can we say that it is not sufficient and go for E?
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