document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=365323>Question 365323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I have to find a degree 3 polynomial whose coefficients are real numbers and with given zeros: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2i ALIGN=MIDDLE  ALT=\"1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2i ALIGN=MIDDLE  ALT=\"1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero, then so is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > so then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%281-2i%29%281%2B2i%29=+0 ALIGN=MIDDLE  ALT=\"-3%281-2i%29%281%2B2i%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then using another example, I came up with this equation. But I'll be honest I don't understand why/how I did this??\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2B2i%29%28x-1-2i%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-1%2B2i%29%28x-1-2i%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then solving through...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-2ix-x%2B1%2B2ix-2i%2B4i%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-x-2ix-x%2B1%2B2ix-2i%2B4i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-2x%2B5%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%2B5%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B3x%5E2-2x%5E2-6x%2B5x%2B15 ALIGN=MIDDLE  ALT=\"x%5E3%2B3x%5E2-2x%5E2-6x%2B5x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which gives me my answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2-x%2B15 ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2-x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, did I do this correctly?\r<BR>\n" );
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document.write( "Thanks so much for your time :)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #260433 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=260433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find a degree 3 polynomial whose coefficients are real numbers and with given zeros: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2i ALIGN=MIDDLE  ALT=\"1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2i ALIGN=MIDDLE  ALT=\"1-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero, then so is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > so then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%281-2i%29%281%2B2i%29=+0 ALIGN=MIDDLE  ALT=\"-3%281-2i%29%281%2B2i%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comment: That is not true; it is not what \"zeroes\" mean.<BR>\n" );
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document.write( "Then using another example, I came up with this equation. But I'll be honest I don't understand why/how I did this??<BR>\n" );
document.write( "Comment: The rule is \"If a is a zero, (x-a) is a factor\"<BR>\n" );
document.write( "--------\r<BR>\n" );
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document.write( "f(x) = (x-(1+2i))(x-(1-2i))(x--3) <BR>\n" );
document.write( "---<BR>\n" );
document.write( "Rearrange to get:<BR>\n" );
document.write( "f(x) = ((x-1)-2i)((x-1)+2i)(x+3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = [(x-1)^2 + 4][x+3]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = [x^2-2x+5][x+3]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = (x^2-2x+5)x + (x^2-2x+5)3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = x^3-2x^2+5x+3x^2-6x+15<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = x^3+x^2-x+15<BR>\n" );
document.write( "============================<BR>\n" );
document.write( "You were correct.<BR>\n" );
document.write( "============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );