I think the answer is B.

The line equation y = (x+a)(x+b) can be written as
Y= X^2 + (a+b)x + ab

From statement 1,
Y= X^2 -x + ab
Not sufficient ,rule out option and d
From statement 2,
-6 = 0^2 + (a+b) 0 + ab
=> ab = -6
Substitution this value in the original equation
Y = X^2 + (a+b)X - 6
Not sufficient,rule out b
Combining 1 & 2,
Y = X^2 -X - 6 ( statement 1 gives you a+b = -1 and statement 2 give ab =-6)
The line will intersect in x axis only when the y coordinate is 0, therefore the equation can be written as
0 = X^2-X-6, solving this equation will give the intersectino points
Therefore 'C' shud be the answer..