document.write( "Question 1181456: How to write a polynomial of degree 3, with integer coefficients that has zeros √3i and 0 \n" ); document.write( "

Algebra.Com's Answer #811352 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "if a polynomial of degree $\"3\"$ has zeros $\"sqrt%283%29%2Ai\"$ and $\"0+\"$ , it also has zero $\"-sqrt%283%29%2Ai\"$ (complex zeros always come in pairs)\r
\n" ); document.write( "\n" ); document.write( "then\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-sqrt%283%29%2Ai%29%28x-%28-sqrt%283%29%2Ai%29%29%28x-0%29\"$ ....expand\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2-%28sqrt%283%29%2Ai%29%5E2%29%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2-3i%5E2%29%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2-3%28-1%29%29%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B3%29%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3%2B3x\"$ \r
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