document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095813>Question 1095813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function of lowest degree with rational coefficients that has -4i, 3 as some of its zeros.\r<BR>\n" );
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document.write( "The possible answers are:<BR>\n" );
document.write( "A) x^4-7x^2+144<BR>\n" );
document.write( "B)x^3-3x^2+16x-48<BR>\n" );
document.write( "C)x^3-4x^2+16x+48<BR>\n" );
document.write( "D)x^4+7x^2-144\r<BR>\n" );
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document.write( "I am struggling with this concept in class, if anyone could possibly help that would be amazing!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710302 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe you're looking at selection B.\r<BR>\n" );
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document.write( "that would be x^3 - 3x^2 + 16x - 48\r<BR>\n" );
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document.write( "the trick here is to know that complex roots always come in pairs.\r<BR>\n" );
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document.write( "the roots shown are -4i and 3.\r<BR>\n" );
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document.write( "the factors from those roots would be (x+4i) and (x-3)\r<BR>\n" );
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document.write( "basically your root says that x = -4i<BR>\n" );
document.write( "add 4i to both sides of that to get x + 4i = 0<BR>\n" );
document.write( "x = -4i is your root<BR>\n" );
document.write( "x + 4i is your factor.\r<BR>\n" );
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document.write( "same with x = 3<BR>\n" );
document.write( "subtract 3 from both sides of that to get x = 3 = 0<BR>\n" );
document.write( "x = 3 is your root.<BR>\n" );
document.write( "x - 3 is your factor.\r<BR>\n" );
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document.write( "simce complex roots always come in pairs, then your other factor has to be x-4i\r<BR>\n" );
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document.write( "that's because the roots are plus or minus 4i.<BR>\n" );
document.write( "from that you get factors of (x + 4i) and (x - 4i)\r<BR>\n" );
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document.write( "the rest is just multiplying your roots to see what equation they become.\r<BR>\n" );
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document.write( "(x + 4i) * (x = 4i) results in x^2 - 16i^2 which becomes x^2 + 16 because i^2 is equal to -1 and -16 * -1 = 16.\r<BR>\n" );
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document.write( "when you multiply (x^2 + 16) * (x-3), you get (x^3 - 3x^2 + 16x - 48).\r<BR>\n" );
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document.write( "that's selection B.\r<BR>\n" );
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document.write( "x+4i and x-4i are called conjugate pairs.<BR>\n" );
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