document.write( "Question 1078910: Find a cubic polynomial in standard form with real coefficients having the given zeros 1 & 1+2i \n" ); document.write( "

Algebra.Com's Answer #693290 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "given:\r
\n" ); document.write( "\n" ); document.write( " $\"1\"$ & $\"1%2B2i\"$ \r
\n" ); document.write( "\n" ); document.write( "if we have $\"1%2B2i\"$ , than we have also $\"1-2i\"$ , complex solutions come always in pairs\r
\n" ); document.write( "\n" ); document.write( "so, we use zero product formula to find equation:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"$ ....plug in $\"x%5B1%5D=1\"$ , $\"x%5B2%5D=1%2B2i\"$ , and $\"x%5B3%5D=1-2i\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-1%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-1%29%28x-1-2i%29%28x-1%2B2i%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2-2x+%2B+2i%281-x%29+%2B+1%29%28x-1%2B2i%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2-2x+%2B+2i%281-x%29+%2B+1%29%28x-1%2B2i%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3+-+3x%5E2+%2B+7x+-+5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+-+3x%5E2+%2B+7x+-+5%29+\"$ \r
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