document.write( "Question 1100942: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.\r
\n" ); document.write( "\n" ); document.write( "7, -11, and 2 + 8i \n" ); document.write( "

Algebra.Com's Answer #715508 by KMST(5328) $\"\"$ $\"About$

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If complex number $\"2+%2B+8i\"$ is a zero of a polynomial with real coefficients,
\n" ); document.write( "so is the conjugate complex number, $\"2+-+8i\"$ .
\n" ); document.write( "So, we know four zeros of the function,
\n" ); document.write( "and for each $\"zero\"$ , there must be a factor of the form $\"x-zero\"$ .
\n" ); document.write( "As a consequence, the simplest polynomial function of minimum degree,
\n" ); document.write( "with real coefficients, and including those four zeros is
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x-%28-11%29%29%28x-%282+%2B+8i%29%29%28x-%282+-+8i%29%29\"$ .
\n" ); document.write( "Now, we just have to simplify and multiply.
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28x-2-+8i%29%28x-2%2B+8i%29\"$
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28%28x-2%29-+8i%29%28%28x-2%29%2B+8i%29\"$
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28%28x-2%29%5E2-+%288i%29%5E2%29\"$
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28x%5E2-4x%2B4-8%5E2%28i%29%5E2%29\"$
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28x%5E2-4x%2B4-64%28-1%29%29\"$
\n" ); document.write( " $\"f%28x%29=%28x-7%29%28x%2B11%29%28x%5E2-4x%2B4%2B64%29\"$
\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B4x-77%29%28x%5E2-4x%2B68%29\"$
\n" ); document.write( " $\"f%28x%29=x%5E4-25x%5E2%2B580x-5230\"$ \n" ); document.write( "

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