GMATPrep Coordinate Geometry Confusing

[shahab03]

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.


LOST

[parallel_chase]

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.