Question

How do you find all the zeros of `f(x) = x^2 - 4x - 60` with its multiplicities?

Answer 1

`f(x)` has zeros at `x=6` and `x=-4` (there are only `2` zeros including multiplicity)

Explanation:

Factoring
`color(white)("XXX")f(x)=x^2-4x-60`

`color(white)("XXXXX")=(x+4)(x-6)`

When `f(x)=0`
either
`color(white)("XXX")(x+4)=0 rarr x=-4`
or
`color(white)("XXX")(x-6)=0 rarr x=+6`

Since `f(x)` is a quadratic (i.e. of degree `2`)
it has (including multiplicity and possible complex values) exactly `2` zeroes.