Answer:
The solutions are:
[tex]x= 0[/tex] and [tex]x= 2[/tex] and [tex]x = -6[/tex]
Step-by-step explanation:
1) Make the function equal to zero
[tex]f(x)=x^3+4x^2-12x = 0[/tex]
2) Take x as a common factor
[tex]x(x^2+4x-12) = 0[/tex]
3) Factor the expression [tex]x^2+4x-12[/tex]
The sought-after factors are such numbers that when multiplying them obtain as result -12 and when adding both numbers obtain as result 4.
The numbers that meet this condition are
6 and -2
Because
[tex]6*(-2) = -12\\\\6 -2 = 4[/tex]
Then the factors are
[tex]x^2+4x-12=(x-2)(x+6)[/tex]
4) Solve the equation for x
[tex]x(x-2)(x+6) = 0[/tex]
The solutions are:
[tex]x= 0[/tex] and [tex]x= 2[/tex] and [tex]x = -6[/tex]
