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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

Respuesta :

irspow
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:

The correct option is c.

Step-by-step explanation:

The given function is

[tex]f(x)=x^3-x^2-12x[/tex]

Taking out the common factors.

[tex]f(x)=x(x^2-x-12)[/tex]

Now, factorize the parenthesis.

[tex]f(x)=x(x^2-4x+3x-12)[/tex]

[tex]f(x)=x(x(x-4)+3(x-4))[/tex]

[tex]f(x)=x(x-4)(x+3)[/tex]

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

[tex]f(x)=0[/tex]

[tex]x(x-4)(x+3)=0[/tex]

Using zero product property, we get

[tex]x=0[/tex]

[tex]x-4=0\Rightarrow x=4[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

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

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