Answer:
The solutions are:
[tex]x=0,\:x=-3,\:x=4[/tex]
Step-by-step explanation:
Given the function
[tex]f(x) = x(x+3)(x - 4)[/tex]
In order to determine the zeros of the function, we substitute f(x) = 0
[tex]0\:=\:x\left(x+3\right)\left(x\:-\:4\right)[/tex]
switch sides
[tex]x\left(x+3\right)\left(x-4\right)=0[/tex]
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
[tex]x=0\quad \mathrm{or}\quad \:x+3=0\quad \mathrm{or}\quad \:x-4=0[/tex]
Thus,
x = 0
and solving x + 3 = 0
x + 3 = 0
subtracting 3 from both sides
x + 3 - 3 = 0 - 3
x = -3
and solving x - 4 = 0
x - 4 = 0
x - 4 + 4 = 0 + 4
x = 4
Therefore, the solutions are:
[tex]x=0,\:x=-3,\:x=4[/tex]
