Question

How do you find the zeros of `f(x) = x^3 – 9x^2 + 20x`?

Answer 1

Factor then recognizing that one of the terms must be equal to zero for the zero of the function:
`color(white)("XX") x=0 or x=4 or x=5`

Explanation:

`x^3-9x^2+20x`
`color(white)("XXX") =x(x^2-9x+20)`

`color(white)("XXX") =x(x-4)(x-5)`

If `f(x)=x^3-9x+20x=0` then
`{("either ",x = 0,),("or",(x-4)=0,rarrx=4),("or",(x-5)=0,rarr x=5):}`