y = (x+a)(x+b) ----------(A)
At the intersection with X axis, y=0
So, We need to solve the equation (x+a)(x+b) = 0
or, x^2 + (a+b)x + ab = 0 ---------------(B)
Statement 1:
a+b = -1
Substituting in B,
=> x^2 - x +ab = 0 --------------(C)
We cannot solve C as ab is unknown
Insufficient.
Statement 2:
The graph intersects y axis at (0, -6)
=> Substituting in (A),
- 6 = (0 + a)(0 + b)
=> ab = -6 ------------(D)
Substituting in B,
x^2 + (a+b)x - 6 = 0 ---------------(E)
We cannot solve E as a+b is unknown.
Insufficient.
Statements 1 and 2 together:
From Statement 1,
a+b = -1,
From Statement 2,
ab = -6
Substituting in (B),
x^2 - x - 6 = 0
This equation can be solved to get x (3,-2).
Thus the points are (3,0) and (-2,0).
Thus 1 and 2 together are sufficient.
Ans C.
scio me nihil scire
