How do you find zeros of #f(x)=x^3-16x#?

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Answer 1 · 2016-11-10T08:53:40

The zeros are #x_1=0#, #x_2=-4# and #x_3=4#. See explanation

To find the zeros we have to solve the equation:

#x^3-16x=0#

#x*(x^2-16)=0#

#x*(x-4)*(x+4)=0#

The product of expressions is zero if any of expressions is zero:

#x=0 vv x-4=0 vv x+4=0#

#x=0 vv x=4 vv x=-4#

Finaly we can write that the equation has 3 solutions:

#x_1=-4#, #x_2=0# and #x_3=4#