Question

Find the zeros, show work f(x)= }{2}" alt="\frac{1}{2}" align="absmiddle" class="latex-formula">x³-x

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Answer 1

The zeros of function are x-s, for which f(x) = 0:

$f(x)=\dfrac{1}{2}x^3-x\\\\f(x)=0\iff\dfrac{1}{2}x^3-x=0\ \ \ \ |\cdot2\\\\x^3-2x=0\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x=0\ \vee\ x^2=2\\\\\boxed{x=0\ \vee\ x=-\sqrt2\ \vee\ x=\sqrt2}$