document.write( "Question 957068: Form a polynomial f(x) with real coefficients having the given degree and zeros:
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Algebra.Com's Answer #584777 by MathLover1(20850) $\"\"$ $\"About$

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$\"f%28x%29\"$ with real coefficients having the given degree and zeros:
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\n" ); document.write( "zeros:
\n" ); document.write( " $\"x%5B1%5D=-4-2i\"$ ;complex roots coming always in pairs, so you also have $\"x%5B2%5D=-4%2B2i\"$
\n" ); document.write( " $\"x%5B3%5D=1\"$ multiplicity 2-double root\r
\n" ); document.write( "\n" ); document.write( "use zero product rule to find $\"f%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-%28-4-2i%29%29%28x-%28-4%2B2i%29%29%28x-1%29\"$ since $\"%28x-1%29\"$ has multiplicity 2 we can square it\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B4%2B2i%29%28x%2B4-2i%29%28x-1%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B8x%2B16-4%28-1%29%29%28x%5E2-2x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B8x%2B16%2B4%29%28x%5E2-2x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B8x%2B20%29%28x%5E2-2x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E4%2B8x%5E3%2B20x%5E2-2x%5E3-16x%5E2-40x%2Bx%5E2%2B8x%2B20\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E4%2B6x%5E3%2B5x%5E2-32x%2B20\"$ \r
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