Answer:
[tex]x=0\\x=4\\x=-2[/tex]
Explanation:
The zeros of a function are all the values of x for which f (x) = 0.
Therefore to find the zeros of the function I must equal f(x) to zero and solve for x.
[tex]f(x) = x(x - 4)(x + 2)=0[/tex]
[tex]x(x - 4)(x + 2)=0[/tex]
We have the multiplication of 3 factors x, (x-4) and (x + 2)
Then the function will be equal to zero when one of the factors is equal to zero, that is:
[tex]x = 0\\(x-4) = 0,\ x = 4\\(x + 2) = 0,\ x = -2[/tex]
Note that [tex]f(x) = x (x - 4) (x + 2)[/tex] is a cubic function of positive principal coefficient, the graph starts from [tex]-\infty[/tex] and cuts to the x-axis at [tex]x = -2[/tex], then decreases and cuts by second once to the x-axis at [tex]x = 0[/tex], it finally cuts the x-axis for the third time at [tex]x = 4[/tex] and then tends to [tex]\infty[/tex]
