document.write( "Question 186246: how do i find the 4th degree polynomial with real coefficients that has zeros of -2, 3, 1+4i, and 1-4i? \n" ); document.write( "
Algebra.Com's Answer #139854 by ankor@dixie-net.com(22740)\"\" \"About 
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how do i find the 4th degree polynomial with real coefficients that has zeros of -2, 3, 1+4i, and 1-4i?
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\n" ); document.write( "Deal with (1 +/- 4i) fir4st
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\n" ); document.write( "x = 1 +/- 4i
\n" ); document.write( "x - 1 = +/-4i
\n" ); document.write( "Square both sides:
\n" ); document.write( "(x-1)^2 = (4i)^2
\n" ); document.write( "x^2 - 2x + 1 = 16i^2
\n" ); document.write( "x^2 - 2x + 1 = 16(-1)
\n" ); document.write( "x^2 - 2x + 1 = -16
\n" ); document.write( "x^2 - 2x + 1 + 16 = 0
\n" ); document.write( "x^2 - 2x + 17
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\n" ); document.write( "x = -2:
\n" ); document.write( "(x^2 - 2x + 17) * (x+2) = x^3 + 13x + 34
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\n" ); document.write( "x = 3
\n" ); document.write( "(x^3 + 13x + 34) * (x-3) = (x^4 - 3x^3 + 13x^2 - 5x - 102) is the 4th degree polynomial \n" ); document.write( "
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