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

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Answer 1 · 2016-02-26T12:29:04

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

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]}

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