document.write( "Question 1157331: Form a polynomial f left parenthesis x right parenthesis with real coefficients having the given degree and zeros.
\n" ); document.write( "Degree 4; zeros: 3+2i ; -5 multiplicity 2
\n" ); document.write( "Enter the polynomial.
\n" ); document.write( "f(x)=a(___)
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Algebra.Com's Answer #780180 by greenestamps(13334) $\"\"$ $\"About$

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\n" ); document.write( "The polynomial is to have real coefficients, so the complex zeros occur in conjugate pairs. So the roots are 3+2i, 3-2i, -5, and -5.

\n" ); document.write( "Use Vieta's theorem to find the quadratic polynomial with roots 3+2i and 3-2i:
\n" ); document.write( " $\"%283%2B2i%29%2B%283-2i%29+=+6\"$
\n" ); document.write( " $\"%283%2B2i%29%283-2i%29+=+9-%28-4%29+=+13\"$

\n" ); document.write( "The quadratic polynomial is

\n" ); document.write( " $\"x%5E2-6x%2B13\"$

\n" ); document.write( "The quadratic polynomial with roots -5 and -5 is

\n" ); document.write( " $\"x%5E2%2B10x%2B25\"$

\n" ); document.write( "The polynomial we want is

\n" ); document.write( " $\"f%28x%29+=+%28x%5E2-6x%2B13%29%28x%5E2%2B10x%2B25%29+=+x%5E4%2B4x%5E3-22x%5E2-20x%2B325\"$

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