Question

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

a. 0, −4, −3
b. 0, −4, 3
c. 0, 4, −3
d. 0, 4, 3

Legit answer plz
this is important

Answer 1

x^3-x^2-12x=0 factor out x

x(x^2-x-12)=0 factor parenthetical expression

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

x(x(x-4)+3(x-4))=0

x(x+3)(x-4)=0

So x=-3, 0, 4

So c) 0, 4, -3

Answer 2

The correct option is c.

Explanation:

The given function is

`f(x)=x^3-x^2-12x`

Taking out the common factors.

`f(x)=x(x^2-x-12)`

Now, factorize the parenthesis.

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

`f(x)=x(x(x-4)+3(x-4))`

`f(x)=x(x-4)(x+3)`

Equate the function equal to 0, to find the zeros of the polynomial function f(x).

`f(x)=0`

`x(x-4)(x+3)=0`

Using zero product property, we get

`x=0`

`x-4=0\Rightarrow x=4`

`x+3=0\Rightarrow x=-3`

The zeros of the polynomial function f(x) are 0,4,-3. Therefore the correct option is c.