document.write( "Question 1071910: Find a polynomial of degree 4 with integer coefficients has zeros 1+i and i, with constant term 6. What is the leading coefficient? \n" ); document.write( "

Algebra.Com's Answer #686952 by Fombitz(32388) $\"\"$ $\"About$

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Real coefficients in a polynomial with complex roots means the roots come in complex conjugate pairs,
\n" ); document.write( " $\"f%28x%29=a%28x-%281%2Bi%29%29%28x-%281-i%29%29%28x-i%29%28x%2Bi%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%5E2-2x%2B2%29%28x%5E2%2B1%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%5E4-2x%5E3%2B3x%5E2-2x%2B2%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"2a=6\"$
\n" ); document.write( " $\"a=3\"$
\n" ); document.write( " $\"highlight%28f%28x%29=3%28x%5E4-2x%5E3%2B3x%5E2-2x%2B2%29%29\"$ \n" ); document.write( "

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