Coordinate geometry

Answer C

GMATGuruNY wrote:

Deepthi Subbu wrote:In the xy-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 intersects the y-axis at (0, -6).

The graph will intersect the x axis when y=0.
Since y = (x+a)(x+b), y=0 when either (x+a) = 0 or (x+b) = 0.
Thus, to determine which x values will make y=0, we need to know the values of a and b.

Statement 1:
2 variables, 1 linear equation, insufficient.

Statement 2:
Substituting x=0 and y=-6 into y = (x+a)(x+b), we get:
-6 = (0+a)(0+b)
-6 = ab.
2 variables, 1 equation, insufficient.

Statements 1 and 2 together:
2 variables, 2 different equations, sufficient.

The correct answer is C.

We can also solve it as below

y = (x+a)(x+b)

for intersecting at x y=0

(x+a)(x+b) = 0

Either x = -a or x = -b so two points will be (-a,0) and (-b,0)

Statement 1
(1) a + b = -1

a = -b -1 will not help us

Statement 2

The graph intersects the y-axis at (0, -6).

means x = 0

y = ab at y =-6
ab = -6 will not help us

a can be 6 & b = -1 or a can be 3 & b = -2 etc. NOT SUFFICIENT

combined both statements
solving for a & b
a= -b -1
ab = -6

gives
a = -3 b = 2 or a = 2 b= -3

so point will (-a,0) & (-b,0) gives us below points

(3,0)(-2,0) or (-2,0) or (3,0)

which are two points as (-2,0) or (3,0)

Answer C