document.write( "Question 652184: Find a polynomial function with real coefficients that has the given zeros.\r
\n" ); document.write( "\n" ); document.write( "3, 1-3i \n" ); document.write( "
Algebra.Com's Answer #407919 by nerdybill(7384)\"\" \"About 
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Find a polynomial function with real coefficients that has the given zeros.\r
\n" ); document.write( "\n" ); document.write( "3, 1-3i
\n" ); document.write( "if you have a complex root, then you know you also have a root that is its conjugate: 1+3i
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\n" ); document.write( "the roots are:
\n" ); document.write( "3, 1-3i, 1+3i
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\n" ); document.write( "If these are the roots, then the factors must be:
\n" ); document.write( "(x-3), (x-(1-3i)), (x-(1+3i))
\n" ); document.write( "or
\n" ); document.write( "(x-3), (x-1+3i), (x-1-3i)
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\n" ); document.write( "multiply all three factors to get your polynomial:
\n" ); document.write( "(x-3)(x-1+3i)(x-1-3i)
\n" ); document.write( "(x-3)(x(x-1-3i)-1(x-1-3i)+3i(x-1-3i))
\n" ); document.write( "(x-3)(x^2-x-3xi-x+1+3i+3xi-3i+9)
\n" ); document.write( "(x-3)(x^2-x-x+1+3i-3i+9)
\n" ); document.write( "(x-3)(x^2-x-x+1+9)
\n" ); document.write( "(x-3)(x^2-2x+10)
\n" ); document.write( "x^2(x-3)-2x(x-3)+10(x-3)
\n" ); document.write( "x^3-3x^2-2x^2+6x+10x-30
\n" ); document.write( "x^3-5x^2+6x+10x-30
\n" ); document.write( "x^3-5x^2+16x-30\r
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