f(x)=(2x+1)(3x-2)
The zero product property says that f(x)=0 when either (2x+1)=0, or (3x-2)=0, or both.
We also know that the zeroes of an equation are the values of x when f(x)=0.
So f(x)=0 when (2x+1)=0 or (3x-2)=0 => x=-1/2 or when x=2/3. which are the roots of f(x).
A. the y-intercepts have nothing to do with the zeroes of f(x).
B. By definition of zero of a function, it is true that the values of x when f(x)=0 are the zeroes of f(x).
C. The zeroes of f(x) are the same as the ones calculated above, so it is true.
D. The x-intercepts of the lines are basically the zeroes of the function f(x), as explained above. So the statement is true.
