document.write( "Question 916425: Form a polynomial F(x) with real coefficients having the given degree and zeros.\r
\n" ); document.write( "\n" ); document.write( "Degree 4 ; Zeros: 2-2i; 4 Multiplicity 2\r
\n" ); document.write( "\n" ); document.write( "F(x)=a(?) \n" ); document.write( "

Algebra.Com's Answer #556069 by josgarithmetic(39617) $\"\"$ $\"About$

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$\"F%28x%29=%28x-%282-2i%29%29%28x-%282%2B2i%29%29%28x-4%29%5E2\"$ , complex roots occur in conjugate pairs.\r
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\n" ); document.write( "\n" ); document.write( "The two factors with the complex roots form a quadratic product which you find through just multiplication:
\n" ); document.write( " $\"%28x-2%2B2i%29%28x-2-2i%29\"$
\n" ); document.write( " $\"%28%28x-2%29%2B2i%29%28%28x-2%29-2i%29\"$
\n" ); document.write( " $\"%28x-2%29%5E2-%284i%5E2%29\"$
\n" ); document.write( " $\"x%5E2-4x%2B4-%28-1%294x%5E2-4x%2B4%2B4\"$
\n" ); document.write( " $\"x%5E2-4x%2B8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Summarizing F:
\n" ); document.write( " $\"highlight%28F%28x%29=%28x%5E2-4x%2B8%29%28x-4%29%5E2%29\"$
\n" ); document.write( "Still in factored form. You can multiply and simplify to arrange in general form for a polynomial of sum of terms. \n" ); document.write( "

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