Question

How use zero product property to solve equations

Answer 1

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"