document.write( "Question 1201306: Find a polynomial with integer coefficients that satisfies the given conditions.\r
\n" ); document.write( "\n" ); document.write( "R has degree 4 and zeros 1 − 2i and 5, with 5 a zero of multiplicity 2.\r
\n" ); document.write( "\n" ); document.write( "R(x)=
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Algebra.Com's Answer #835605 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "Complex roots come in conjugate pairs, so the unspecified zero is 1 + 2i\r
\n" ); document.write( "\n" ); document.write( "\"+R%28x%29+=+%28x-5%29%5E2+%28x-1%2B2i%29%28x-1-2i%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"+highlight%28+R%28x%29+=+x%5E4-12x%5E3%2B50x%5E2-100x+%2B+125+%29+\"\r
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\n" ); document.write( "\n" ); document.write( "Details:
\n" ); document.write( "\"+R%28x%29+=+%28%28x-5%29%5E2%29++%28%28x-1%2B2i%29%28x-1-2i%29%29+\"
\n" ); document.write( "Muliplying each factor (shown within paren's):
\n" ); document.write( "\"+R%28x%29+=+%28x%5E2-10x%2B25%29%28x%5E2-2x%2B5%29+\"
\n" ); document.write( "Now multiplying the two trinomials:
\n" ); document.write( "\"+R%28x%29+=+%28x%5E4-2x%5E3%2B5x%5E2-10x%5E3%2B20x%5E2-50x%2B25x%5E2-50x%2B125%29+\"
\n" ); document.write( "Combining like terms:
\n" ); document.write( "\"+R%28x%29+=+x%5E4-12x%5E3%2B50x%5E2-100x%2B125+\"
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