document.write( "Question 163213: Finding zeros of a function:
\n" ); document.write( "f(x) = 1/2x^3 - x \n" ); document.write( "

Algebra.Com's Answer #120294 by orca(409) $\"\"$ $\"About$

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To find the zeros of the function, you need to solve the equation:
\n" ); document.write( " $\"%281%2F2%29x%5E3-x=0\"$
\n" ); document.write( "Factoring the left side, we have
\n" ); document.write( " $\"x%28%281%2F2%29x%5E2+-+1%29=0\"$
\n" ); document.write( "So
\n" ); document.write( " $\"x+=+0\"$ or $\"%281%2F2%29x%5E2-1=0\"$
\n" ); document.write( "Solving $\"%281%2F2%29x%5E2-1=0\"$ , we obtain:
\n" ); document.write( " $\"%281%2F2%29x%5E2=1\"$
\n" ); document.write( " $\"x%5E2=2\"$
\n" ); document.write( " $\"x+=+sqrt%282%29\"$ or $\"x=-sqrt%282%29\"$
\n" ); document.write( "So the zeros of the function are $\"0\"$ , $\"sqrt%282%29\"$ and $\"-sqrt%282%29\"$
\n" ); document.write( " \n" ); document.write( "

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