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 answer is C.

Can someone explain how to solve this question?

Hi,

The graph is y = (x+a) (x+b)

To find out at what point this graph intersect x-axis approach as follows:-

When a graph intersect x-axis, the intersection point would be (x,0).
When a graph intersect y-axis, the intersection point would be (0,y).


Applying the same to equation , we have
=> (x+a) (x+b) = 0
=> x^2 + (a+b)x + ab = 0
The two points can be determined by solving this equation or by finding out the values of a and b.


(1) a+b = -1 , we still dont know the values of a and b. INSUFFICIENT

(2) The graph intersect the y-axis at (0,-6).
So the graph y = (x+a) (x+b) can be rewritten as
-6 = (0 +a) (0+b)
-6 = ab. we still dont know the values of a and b. INSUFFICIENT



Combing (1) and (2) , we have a + b = -1 and ab = -6 ,

The two points would be x^2 + (a+b)x + ab = 0
x^2 -x -6 =0
x^2 -3x +2x -6 =0
x(x-3) +2(x-3) =0
(x-3) (x+2) = 0


So two points where the graph intersect is (3,0) and (-2,0). Hence SUFFICIENT using (1) and (2) so C.

Thanks

well played.