document.write( "Question 1113596: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
\n" ); document.write( "3, -13, and 5 + 4i \n" ); document.write( "

Algebra.Com's Answer #728664 by math_helper(2461) $\"\"$ $\"About$

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The zeros at 3 and -13 result in factors (x-3)(x+13)\r
\n" ); document.write( "\n" ); document.write( "The zero at 5+4i will be one of two zeros, where the 2nd zero is at 5-4i (complex roots come in conjugate pairs). \r
\n" ); document.write( "\n" ); document.write( "Assuming the form $\"+x%5E2+%2B+bx+%2B+c+=+0+\"$ and using the quadratic formula
\n" ); document.write( " $\"+-%28b%2F2a%29+%2B-+sqrt%28%28b%5E2-4ac%29%29%2F%282a%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+++-b%2F%282a%29+=++5+\"$ —> $\"+b+=+-10+\"$
\n" ); document.write( " $\"+++sqrt%28%28b%5E2-4%2A1%2Ac%29%29%2F%282%2A1%29+=+4i+\"$ —> $\"+%28100-4c%29%2F4+=+-16+\"$ —> $\"+100-4c+=+-64+\"$
\n" ); document.write( " —> $\"+c+=+41+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2+-+10x+%2B+41+\"$ generates zeros at $\"+5+%2B-+4i+\"$ \r
\n" ); document.write( "\n" ); document.write( "—
\n" ); document.write( "Putting it all together: $\"+f%28x%29+=+%28x+-+3%29%28x+%2B+13%29%28x%5E2+-+10x+%2B+41%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "…in expanded form: $\"+highlight%28f%28x%29+=+x%5E4+-+98x%5E2+%2B+800x+-+1599%29+\"$
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