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)
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y = (x+a)(x+b)
expanding it, u get
y= x^2+(a+b)x+(ab) ----- (A)
from option(1) we get value of only a+b. we still need ab, hence it alone is insufficient.
from option(2)
by putting x=0 & y=-6 in equation (A), we get
-6=0+0+ab
ie ab= -6
by using both options together in (A), we get
y=x^2 -1x -6
this line will intersect the x-axis at a point where y=0
ie
0=x^2 -1x -6
x^2 -3x +2x -6 = 0
(x-3)(x+2)=0
ie x=3 or x=-2
note that we are asked to find
In the xy plane at what two points does the graph of y = (x+a)(x+b) intersect the x-axis.
Hence the two points are (3,0) & (-2,0)
So (C) is the correct answer
