karthikpandian19 wrote:In the XY plane, at what 2 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)

When the graph intersects the x-axis, the intersection point will be (x, 0). This implies (x + a)(x + b) = 0 or x²+ (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 x² - 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, the correct answer is C.