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)
1) a+b=-1
2) The graph intersects the y-axis at (0,-6)
Is it "at what point" or "at what two points"?
When the graph intersects the x-axis, the intersection point will be (x, 0). This implies (x + a)(x + b) = 0 or x^2 + (a + b)x + ab = 0.
(1) a + b = -1 does not gives us the values of a and b.
So, (1) is NOT SUFFICIENT.
(2) When the graph intersects the y-axis, the intersection point is (0, y). So, -6 = (0 + a)(0 + b) implies ab = -6. Again we don't get a unique answer.
So, (2) is NOT SUFFICIENT.
Combining (1) and (2), a + b = -1 and ab = -6 implies x^2 - x - 6 = 0 or (x - 3)(x + 2) = 0 or x -2, 3
So, the graph intersects at (-2, 0) and (3, 0). Assuming that it is two points, [spoiler]the correct answer is (C)[/spoiler].
