document.write( "Question 1178029: Find an nth- degree polynomial function with real coefficients satisfying the given conditions.
\n" ); document.write( "n=3
\n" ); document.write( "3 and 5i are zeros
\n" ); document.write( "f(-1) = -312\r
\n" ); document.write( "\n" ); document.write( "F(x)= \n" ); document.write( "
Algebra.Com's Answer #807208 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "Real coefficients with roots 3 and 5i means -5i is another root. Since the polynomial is degree 3, those are the only roots.

\n" ); document.write( "The linear factor corresponding to the root 3 is (x-3); the quadratic factor corresponding to the roots 5i and -5i is (x^2+25).

\n" ); document.write( "So f(x) is of the form

\n" ); document.write( "\"f%28x%29+=+a%28x-3%29%28x%5E2%2B25%29\"

\n" ); document.write( "Determine the constant a knowing that f(-1)=-312:

\n" ); document.write( "\"f%28-1%29+=+a%28-4%29%2826%29+=+-104a+=+-312\"
\n" ); document.write( "\"a+-312%2F-104+=+3\"

\n" ); document.write( "The function is

\n" ); document.write( "\"f%28x%29+=+-3%28x-3%29%28x%5E2%2B25%29\"
\n" ); document.write( "\"f%28x%29+=+-3x%5E3%2B9x%5E2-75x%2B225\"

\n" ); document.write( " \n" ); document.write( "
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