The zero product property says that A*B = 0, then A = 0 or B = 0
In words: if two numbers multiply to 0, then one (or both) of the values must be zero.
So in terms of algebra, if we had
-0.2*(x-1.9)*(x-3.5) = 0
then
x-1.9 = 0 or x-3.5 = 0
Now solve each individual equation for x
x-1.9 = 0
x-1.9+1.9 = 0+1.9 ... adding 1.9 to both sides
x = 1.9
x-3.5 = 0
x-3.5+3.5 = 0+3.5 .... adding 3.5 to both sides
x = 3.5
The two solutions are x = 1.9 or x = 3.5
These two x values, when plugged into f(x), will make f(x) = 0
These are the x intercepts because this is where the graph crosses the x axis.
Note: "root" is another term for "x intercept"
