Question

How do you find all the zeros of `x^2 + 24 = 11x` with its multiplicities?

Answer 1

This equation has solutions `x=8` and `x=3` (both with multiplicity `1`).

Explanation:

Subtract `11x` from both sides to get:

`x^2-11x+24 = 0`

Note that `11=8+3` and `24=8*3`.

So we find:

`0 = x^2-11x+24 = (x-8)(x-3)`

Hence zeros `x=8` and `x=3` (both with multiplicity `1`).