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Cordinate Geometry

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Cordinate Geometry

by B166418 » Wed Nov 07, 2012 8:07 pm
In a XY-plane at what two points does the graph Y=(x+a)(X+b)intersect the X-axis

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


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
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by FLUID » Wed Nov 07, 2012 11:03 pm
B166418 wrote:In a XY-plane at what two points does the graph Y=(x+a)(X+b)intersect the X-axis

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


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:


The graph is y = (x+a) (x+b)

At what point graph intersect x-axis :-

When a graph intersect x-axis, the intersection point would be (x,0).
When a graph intersect y-axis, the intersection point would be (0,y).


=> (x+a) (x+b) = 0 (since y =0 when graph intersects x-axis)
=> x^2 + (a+b)x + ab = 0

you can solve this equation only if you know the values of a and b.


(1) a+b = -1 , we still dont know the values of a and b. INSUFFICIENT

(2) The graph intersect the y-axis at (0,-6).
So the graph y = (x+a) (x+b) can be rewritten as
-6 = (0 +a) (0+b)
-6 = ab. we still dont know the values of a and b. INSUFFICIENT



Combing (1) and (2) , we have a + b = -1 and ab = -6 ,

The two points would be x^2 + (a+b)x + ab = 0
x^2 -x -6 =0
x^2 -3x +2x -6 =0
x(x-3) +2(x-3) =0
(x-3) (x+2) = 0


Two points where the graph intersect is (3,0) and (-2,0).
Hence SUFFICIENT using (1) and (2) so C.
Thanks,

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