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]}