Question

What are the zeros of the function? f(x)=x3+4x2−12x

Answer 1

Set the function equal to 0 and solve for

x=0,2,-6

Answer 2

The solutions are:

`x= 0` and
`x= 2` and
`x = -6`

Explanation:

1) Make the function equal to zero

`f(x)=x^3+4x^2-12x = 0`

2) Take x as a common factor

`x(x^2+4x-12) = 0`

3) Factor the expression
`x^2+4x-12`

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

`6*(-2) = -12\\\\6 -2 = 4`

Then the factors are

`x^2+4x-12=(x-2)(x+6)`

4) Solve the equation for x

`x(x-2)(x+6) = 0`

The solutions are:

`x= 0` and
`x= 2` and
`x = -6`