y=(x+a)(x+b)
when intersects at y,
-6=ab..eqn 1

given that a+b=1..eqn 2
solve 1 & 2
we get b=3,a=-4 and b=-2 and a=3

when intersect at x,
y will be 0

0=(x+a)(x+b)
x = -a,-b

point is (-a,0) or (-b,0)

-6=3.(-2)
b=3,a=-2

x=2,-3

both info is reqd to solve

Take x^2 + (a + b) x + a b = 0 ready, to get to know the points where it intersects the x-axis.

(1) reduces the equation to x^2 + x + a b = 0. With a b not known, this alone is insufficient.

(2) helps us take a b = -6 and reduces the equation to x^2 + (a + b) x - 6. With a + b not known, this alone is insufficient.

Merger makes us have x^2 + x - 6 = 0, whose discriminant (1)^2 - 4 (1) (-6) = 25 > 0, so real, rational and different roots are also guaranteed. Now C surely is the right answer.