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

Feb 13, 2016

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) =$\left(x - 8\right) \left(x - 5\right)$

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

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