document.write( "Question 362448: Find the polynomial P(x) having real coefficients, with the degree and zeroes indicate. Assume that lead coefficient is 1. Recall (a+bi)(a-bi)=a2+b2 (the last one is read a squared + b squared). \r
\n" ); document.write( "\n" ); document.write( "degree4, x=-1, x=1+2i. \n" ); document.write( "

Algebra.Com's Answer #258296 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Since $\"x=1%2B2i\"$ is a zero so is $\"x=1-2i\"$ since complex solutions only come in complex conjugate pairs.
\n" ); document.write( "However since the degree is 4, without additional information on the other real root, you can't determine the polynomial.
\n" ); document.write( "Just for illustration assume the fourth root is $\"x=a\"$ .
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\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x-a%29%28x-%281%2B2i%29%29%28x-%281-2i%29%29\"$
\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x-a%29%28x%5E2-2x%2B5%29\"$
\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B%281-a%29x-a%29%28x%5E2-2x%2B5%29\"$
\n" ); document.write( " $\"highlight%28f%28x%29=x%5E4-%28a%2B1%29x%5E3%2B%28a%2B3%29x%5E2-%283a-5%29x-5a%29\"$
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