Hi, there. I'm happy to give some help on this.
In the x-y plane, at what two points does the graph of y = (x-a)(x-b) intersect the x-axis?
(1) a = b = -1
(2) The graph intersect the y-axis at (0, -6)
First, the prompt:
In the x-y plane, at what two points does the graph of y = (x-a)(x-b) intersect the x-axis?
This graph is a parabola (if you FOIL out the expressions, you will get an x^2, sure sign of a parabola). The roots are where the factors equal zero:
(x-a) = 0 ---> x = -a
(x-b) = 0 ---> x = -b
So, the question "where does the graph intersect the x-axis?" boils down to the question: what are the values of a & b.
Statement #1:
a = b = -1
One equation, two unknowns. Not enough information. Statement #1, by itself, is
insufficient.
Statement #2:
The graph intersect the y-axis at (0, -6)
Plug in the values x = 0 and y = 6, and this yields the equation -6 = ab. Again, one equation, two unknowns. Not enough information. Statement #2, by itself, is
insufficient.
Combined Statements #1 & #2:
This gives us two equations with two unknowns, which opens the possibility of solving for a and b.
(i) a + b = -1
(ii) ab = -6
In order for the product to be negative, one must be positive and one must be negative. In order for their sum to be negative, the number with the larger absolute value must be negative. The only possibility is that one of the numbers is -3 and one is +2 (it doesn't matter at all which we call "a" and which we call "b"). Since we know a & b, we know the x-intercept. Combined, the statements are
sufficient.
Answer =
C
Here's a similar DS questions:
https://gmat.magoosh.com/questions/954
When you submit your answer to this, the following page will have a complete video solution.
Does all this make sense? Please let me know if you have any further questions.
Mike
Both num
