Question

What are the zeros of the polynomial function`f(x) = x^3 – x^2 - 12x`?

Answer 1

The zeros occur at `x in {0,4,-3}`

Explanation:

Given
`color(white)("XXX")f(x)=x^3-x^2-12x`

Factoring:
`color(white)("XXX")f(x)=x(x^2-x-12)`

`color(white)("XXXXX")=x(x-4)(x+3)`

The zeroes of a function are the values of `x` for which the function's value is zero.

`color(white)("XXX")f(x)=x(x-4)(x+3)=0`
implies
`color(white)("XXX")`either
`color(white)("XXXXX")x=0`
`color(white)("XXX")`or
`color(white)("XXXXX")(x-4)=0 rarr x=4`
`color(white)("XXX")`or
`color(white)("XXXXX")(x+3)=0 rarr x=-3`