document.write( "Question 977338: My question is:\r
\n" ); document.write( "\n" ); document.write( "Form a polynomial f(x) with real coefficients having the given degree and zeros\r
\n" ); document.write( "\n" ); document.write( "Degree 5; zeros: -6; -i; -3+1\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #598871 by Boreal(15235)\"\" \"About 
You can put this solution on YOUR website!
The complex roots are conjugate
\n" ); document.write( " 5 roots are -i, +i, 3-i, 3+i, and -6\r
\n" ); document.write( "\n" ); document.write( "(x+6)(x^2+1)
\n" ); document.write( "for the other, (1/2)[-b +/- sqrt (b^2-4ac)].=-6 for b and sqrt (36-40)=(1/2)(-6 +/-sqrt (-4)
\n" ); document.write( "That is (1/2) (-6+/-2i)=-3 +/- i
\n" ); document.write( "This requires -4ac=-40 or ac=10. Let a=1 and c= 10\r
\n" ); document.write( "\n" ); document.write( "so the last polynomial factor is x^2+6x+10 \r
\n" ); document.write( "\n" ); document.write( "The polynomial would be (x+6)(x^2+1)(x^2+6x+10)\r
\n" ); document.write( "\n" ); document.write( "Multiplying it out, I get
\n" ); document.write( "x^5+12x^4+47x^3+72x^2+46x+60\r
\n" ); document.write( "\n" ); document.write( "\"graph%28300%2C300%2C-10%2C5%2C-500%2C500%2Cx%5E5%2B12x%5E4%2B47x%5E3%2B72x%5E2%2B46x%2B60%29\"
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