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

1 Answer
Nov 10, 2016

Answer:

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

Explanation:

To find the zeros we have to solve the equation:

#x^3-16x=0#

#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#