g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?
Choices:
A:$f$ and $g$ share the same root(s).
B:$f$ and $g$ share one root in common but each have another root that is not shared.
C:$f$ and $g$ share no roots in common.
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?
Choices:
A:$f$ and $g$ share the same root(s).
B:$f$ and $g$ share one root in common but each have another root that is not shared.
C:$f$ and $g$ share no roots in common.
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?
Choices:
A:$f$ and $g$ share the same root(s).
B:$f$ and $g$ share one root in common but each have another root that is not shared.
C:$f$ and $g$ share no roots in common.