Answer
$0,7$ and $-7$
Work Step by Step
The given function is
$\Rightarrow y=x^3-49x$
Substitute $0$ for $y$.
$\Rightarrow 0=x^3-49x$
Factor out $x$.
$\Rightarrow 0=x(x^2-49)$
$\Rightarrow 0=x(x^2-7^2)$
Use difference of two squares pattern.
$\Rightarrow 0=x(x-7)(x+7)$
Use zero product property.
$\Rightarrow x=0$ or $x-7=0$ or $x+7=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=7$ or $x=-7$
Hence, the zeros of the function are $0,7$ and $-7$.
