Question

How do you find the zeros of the polynomial function `f(x)=x^3-13x^2+40x`?

Answer 1

Zeros of the polynomial function are `0`, `5` and `8`.

Explanation:

To find the zeros of the polynomial function `f(x)=x^3−13x^2+40x`, We factorize it.

It is obvious that `x` is a factor and hence the polynomial function can be written as `f(x)=x(x^2−13x+40)`.

It is observed that `8` and `5` are two factors of `40` whose sum is `13`and hence `x^2−13x+40`, can be factorized as follows

`x^2−13x+40` = `x^2−5x-8x+40` = `x(x-5)−8(x-5)` =`(x-8)(x-5)`

And hence factors of the polynomial function `f(x)=x^3−13x^2+40x` are `x(x-8)(x-5)`

Hence zeros of the polynomial function are `0`, `5` and `8`.