document.write( "Question 890111: how do you find the complex zeros of the polynomial function.\r
\n" ); document.write( "\n" ); document.write( "f(x)=x^3 + 125 \n" ); document.write( "

Algebra.Com's Answer #538699 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
Either factor the expression or use Rational Roots Theorem. You have the sum of cubes.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B125=x%5E3%2B5%5E3=%28x%2B5%29%28x%5E2-5x%2B5%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Check the quadratic factor for the roots of +- 1, +-5, or +- 25. You can instead, just find its roots using the general solution to quadratic formula.\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%285%2B-+sqrt%2825-4%2A25%29%29%2F%282%29\"$
\n" ); document.write( " $\"x=%285%2B-+sqrt%28-75%29%29%2F2\"$
\n" ); document.write( " $\"x=5%2F2%2B-+%281%2F2%29%2A5sqrt%28-3%29\"$
\n" ); document.write( " $\"highlight%28x=5%2F2%2B-+%285%2F2%29i%2Asqrt%283%29%29\"$ ---these are TWO of the roots.\r
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\n" ); document.write( "\n" ); document.write( "Obviously the first root is $\"highlight%28x=-5%29\"$ . \n" ); document.write( "

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