document.write( "Question 1099280: Find a polynomial with integer coefficients that satisfies the given conditions.
\n" ); document.write( "U has degree 5, zeros 1/2, −4, and −i, and leading coefficient 4; the zero −4 has multiplicity 2. \n" ); document.write( "
Algebra.Com's Answer #713716 by KMST(5328)\"\" \"About 
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Each zero \"x%5Bk%5D\" means the factored form of the polynomial has
\n" ); document.write( "as many factors of the form \"%28x+-+x%5Bk%5D%29\" as the multiplicity of the zero.
\n" ); document.write( "That means that the factored form of the polynomial includes
\n" ); document.write( "\"%28x-1%2F2%29%28x%2B4%29%5E2%28x%2BI%29\"
\n" ); document.write( "For each complex zero, the conjugate complex number is also a zero.
\n" ); document.write( "That means that \"i\" is also a zero, and that \"%28x-i%29\" also appears as a factor.
\n" ); document.write( "So far we have the factors
\n" ); document.write( "\"%28x-1%2F2%29%28x%2B4%29%5E2%28x%2Bi%29%28x-i%29\" ,
\n" ); document.write( "accounting for the degree 5,
\n" ); document.write( "with \"1\" for a leading coefficient.
\n" ); document.write( "We need to include \"4\" as a factor to have 4 for a leading coefficient.
\n" ); document.write( "The polynomial is
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