document.write( "Question 819539: Write a third degree polynomial function y=P(x) with rational coefficients so that P(x)=0 has the given roots. \r
\n" ); document.write( "\n" ); document.write( "3, 6+i \n" ); document.write( "

Algebra.Com's Answer #493143 by josgarithmetic(39617) $\"\"$ $\"About$

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There is one more root; include 6-i as one of them.\r
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\n" ); document.write( "\n" ); document.write( " $\"P%28x%29=0=%28x-3%29%28x-%286%2Bi%29%29%28x-%286-i%29%29\"$
\n" ); document.write( " $\"P%28x%29=%28x-3%29%28x-6-i%29%28x-6%2Bi%29\"$
\n" ); document.write( " $\"%28x-3%29%28%28x-6%29-i%29%28%28x-6%29%2Bi%29\"$ , recognize the difference of two squares for the result, and that i*i=-1,
\n" ); document.write( " $\"%28x-3%29%28%28x-6%29%5E2%2B1%29\"$
\n" ); document.write( " $\"%28x-3%29%28x%5E2-12x%2B36%2B1%29\"$
\n" ); document.write( " $\"%28x-3%29%28x%5E2-12x%2B37%29\"$
\n" ); document.write( "and you can finish the multiplication for the two polynomial factors. \n" ); document.write( "

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