Question

What are the zeros of the polynomial function `f(x) = x(2x-1)^2(x-4)^3`?

Answer 1

If a multiplication ends in a zero, then (at least) one of the factors must be zero.

Explanation:

So we have three possibilities:
(1)
`x=0`
(2)
`(2x-1)^2=0->2x-1=0->x=1//2`
(3)
`(x-4)^4=0->x-4=0->x=4`
graph{x(2x-1)^2(x-4)^3 [-14.23, 14.25, -7.12, 7.13]}