document.write( "Question 306836: Find an nth degree polynomial function with real coefficients satisfying the given conditions n=4,3, -1/3 and 1+2i are zeros: f(1) = 64 \n" ); document.write( "

Algebra.Com's Answer #219515 by Fombitz(32388) $\"\"$ $\"About$

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Complex roots always occur in complex conjugate pairs.
\n" ); document.write( "Since (1+2i) is a solution, (1-2i) is also a solution.
\n" ); document.write( " $\"f%28x%29=A%28x-4%29%28x-3%29%28x%2B1%2F3%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29\"$
\n" ); document.write( " $\"f%281%29=A%281-4%29%281-3%29%281%2B1%2F3%29%281-1-2i%29%281-1%2B2i%29=64\"$
\n" ); document.write( " $\"A%28-3%29%284%2F3%29%28-2i%29%282i%29=64\"$
\n" ); document.write( " $\"A%28-4%29%28-4i%5E2%29=64\"$
\n" ); document.write( " $\"A%28-16%29=64\"$
\n" ); document.write( " $\"A=-4\"$
\n" ); document.write( " $\"f%28x%29=-4%28x-4%29%28x-3%29%28x%2B1%2F3%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29\"$ \n" ); document.write( "

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