Question

How do you find all the zeros of `f(x) = (x-11)(x-5)(x-1)(x+5)`?

Answer 1

`x=-5,1,5,11`

Explanation:

Zeros occur when `f(x)=0`. Graphically, zeros are the spots when a graph crosses the `x`-axis.

Set `f(x)=0`.

`(x-11)(x-5)(x-1)(x+5)=0`

Here, we have four terms being multiplied and equalling `0`. Thus, any one of these terms can equal `0` at any time.

`x-11=0" "=>" "x=11`

`x-5=0" "=>" "x=5`

`x-1=0" "=>" "x=1`

`x+5=0" "=>" "x=-5`

These are the function's four zeros. Graphically represented:

graph{(x-11)(x-5)(x-1)(x+5) [-10, 15, -1100, 700]}