The question is asking for the x-intercepts of y=(x+a)(x+b). We know that x-intercepts can be solved for by substituting 0 for y. So we're left with:
0=(x+a)(x+b)
The solutions to this equation are -a and -b. So essentially, the question is asking you to find -a and -b. Or, more simply, just a and b. (If you can find a and b, you'll know -a and -b.)
(1) a + b = -1
We have one equation and two unknowns --> insufficient. There are an infinite number of possibilities.
(2) This tells us that (0, -6) is a solution point of the original equation, y=(x+a)(x+b). Substituting, we get -6=ab --> insufficient. Again, there are an infinite number of possibilities.
(1&2) Solve the resulting system of equations.
a + b = -1 ==> a = -b - 1
ab = -6
(-b - 1)b = -6 (substituting)
0=b^2 + b - 6
b = 2, b = -3
When b = 2, a = -3.
When b = -3, a = 2.
So the x-intercepts are (-2, 0) and (3, 0). Sufficient.
Rey Fernandez
Instructor
Manhattan GMAT
