Question

How do you find all the zeros of `f(x) = x^3 – 10x^2 + 24x`?

Answer 1

`f(x)` has zeros `0, 4, 6`

Explanation:

`f(x) = x^3-10x^2+24x`

Since all of the terms are divisible by `x`, we can separate that out as a factor. Then we can factor the remaining quadratic using the facts that `4+6=10` and `4*6=24`...

`x^3-10x^2+24x = x(x^2-10x+24) = x(x-4)(x-6)`

Hence zeros:

`x = 0`, `x=4` and `x=6`.