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

Feb 26, 2016

$x = - 5 , 1 , 5 , 11$

#### Explanation:

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

Set $f \left(x\right) = 0$.

$\left(x - 11\right) \left(x - 5\right) \left(x - 1\right) \left(x + 5\right) = 0$

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

$x - 11 = 0 \text{ "=>" } x = 11$

$x - 5 = 0 \text{ "=>" } x = 5$

$x - 1 = 0 \text{ "=>" } x = 1$

$x + 5 = 0 \text{ "=>" } x = - 5$

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

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