co-ordinate geometry - GMAT Prep

[Pugalenthi]

Hi, I am stumped on this question (particularly seeing x^2 in the equation whereas the line equation is y = mx + b)...any explanation would be much appreciated.

In the X-Y plane, at what 2 points does the graph y=(x+a)(x+b) intersect the X-axis?
(1)a + b = -1
(2) the graph intersects the Y-axis at (0,-6)

The answer is C.

[Anurag@Gurome]

In the X-Y plane, at what 2 points does the graph y=(x+a)(x+b) intersect the X-axis?
(1)a + b = -1
(2) the graph intersects the Y-axis at (0,-6)

The equation given in the question does not represent a straight line. But we do not need to know what does it represent. The points where the graph of the equation intersects the X-axis will have zero as the y-coordinate.

Let's see for what values of x, y becomes zero.
--> (x + a)(x + b) = 0
Hence, x = -a and x = -b

Hence, the points where the graph intersects the X-axis are (-a, 0) and (-b, 0)

Statement 1: a and b can have many values --> Not sufficient

Statement 2: Hence, at x = 0, y = -6
Therefore, -6 = (0 + a)(0 + b) ---> ab = -6

a and b can have many values.

Not sufficient

1 & 2 Together: (a + b) = -1 and ab = -6
Now, y = (x + a)(x + b) = (x² + (a + b)x + ab) = (x² - x - 6) = (x + 2)(x - 3)

Hence, the graph intersects the X-axis at (-2, 0) and (3, 0)

Sufficient

The correct answer is C.