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)
1) a+b= -1
2) The graph intersects the y-axis at ( 0, -6)
Given: y = (x + a)(x + b)bobdylan 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)
Implies the graph intersects x-axis at x = -a or x = -b.
Thus we have to find the values of a and b.
Statement 1: (a + b) = -1
Infinite numbers of values are possible for a and b.
Not sufficient.
Statement 2: The graph intersects y-axis at (0, -6)
For x = 0, y = (0 + a)(0 + b) = ab = -6
Infinite numbers of values are possible for a and b.
Not sufficient.
1 and 2 Together: (a + b) = -1 and ab = -6
Now, (a - b)² = (a + b)² - 4ab = (-1)² - 4*(-6) = 25
=> (a - b) = ±5
Thus, either (a = 2, b = -3) or (a = -3, b = 2)
In both of the cases the graph intersects x-axis at x = -3 and x = 2.
Sufficient.
The correct answer is C.
