In the xy-plane, at what point 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)
per
https://www.beatthegmat.com/another-gmat ... t8583.html
We are looking for the x-intercept(s).
I. a+b = -1
y = x^2 +ax +bx +ab <<< WHA[/color]T IS THIS?
-We have two equations and 4 unknowns. Cannot solve this. This is not sufficient.
-Answer is B,C, or E.
II. The graph intersects the Y-axis at (0, -6)
-6 = (0)^2 + a(0) + b(0) + ab
-6 = ab
y = x^2 +ax +bx +ab
-We have two equations and 4 unknowns still. Cannot solve this. This is not sufficient.
-Answer is C or E.
Using I and II...
a + b = -1
ab = -6
-We have two equations and 2 unknowns now. This can be solved. You CAN find the x-intercept(s)
Answer is C.
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Though the method posted is perfect,
Here is a simpler version very similar to the above method but easier to understand
y=(x+a)(x+b)
Statement I and II are clearly insufficient.
x^2+ax+bx+ab
a+b = -1
ab = -6 [from second statement]
x^2 - x -6 = 0
(x-3)(x+2) =0
Therefore the two points are
(3,0) and (-2,0) because in both cases we know that y has to be 0.
Hope this helps.
Here is a simpler version very similar to the above method but easier to understand
y=(x+a)(x+b)
Statement I and II are clearly insufficient.
x^2+ax+bx+ab
a+b = -1
ab = -6 [from second statement]
x^2 - x -6 = 0
(x-3)(x+2) =0
Therefore the two points are
(3,0) and (-2,0) because in both cases we know that y has to be 0.
Hope this helps.