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

Question

6095 views around the world

You can reuse this answer
Creative Commons License

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 $x_3=4$