document.write( "Question 915235: Construct a polynomial with the following properties: third degree, real coefficients, y-intercept is -52, zeros are -1, and 5+i. \n" ); document.write( "

Algebra.Com's Answer #555544 by Fombitz(32388) $\"\"$ $\"About$

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A polynomial with real coefficients has roots that are complex conjugates pairs.
\n" ); document.write( "So then,
\n" ); document.write( " $\"f%28x%29=a%28x%2B1%29%28x-%285%2Bi%29%29%28x-%285-i%29%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%2B1%29%28x%5E2-10x%2B26%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%5E3-9x%5E2%2B16x%2B26%29\"$
\n" ); document.write( "Then, when $\"x=0\"$ , $\"f%280%29=-52\"$
\n" ); document.write( " $\"a%280-0%2B0%2B26%29=-52\"$
\n" ); document.write( " $\"a=-2\"$
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\n" ); document.write( " $\"f%28x%29=-2x%5E3%2B18x%5E2-32x-52%29\"$ \r
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