Xy plane

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Jan 06, 2012 3:46 pm

In the XY plane, at what 2 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)

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Source: Beat The GMAT — Problem Solving | Fri Jan 06, 2012 3:46 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Jan 06, 2012 4:15 pm

I posted a solution here:

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santhoshsram: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Oct 26, 2011 2:30 pm; Thanked: 7 times

by santhoshsram » Fri Jan 06, 2012 4:16 pm

karthikpandian19 wrote:In the XY plane, at what 2 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)

Discussed here in the DS forum https://www.beatthegmat.com/x-a-x-b-t36075.html

-- Santhosh S

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Jan 06, 2012 9:54 pm

karthikpandian19 wrote:In the XY plane, at what 2 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)

When the graph intersects the x-axis, the intersection point will be (x, 0). This implies (x + a)(x + b) = 0 or xÂ²+ (a + b)x + ab = 0.

(1) a + b = -1 does not gives us the values of a and b.
So, (1) is NOT SUFFICIENT.

(2) When the graph intersects the y-axis, the intersection point is (0, y). So, -6 = (0 + a)(0 + b) implies ab = -6. Again we don't get a unique answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), a + b = -1 and ab = -6 implies xÂ² - x - 6 = 0 or (x - 3)(x + 2) = 0 or x -2, 3
So, the graph intersects at (-2, 0) and (3, 0).

Assuming that it is two points, the correct answer is C.

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