document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=104483>Question 104483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I have the following multiple choice question:<BR>\n" );
document.write( "Find an nth degree polynomial function with real coefficients satisfying the given conditions.  <BR>\n" );
document.write( "n = 3;  - 4 and i are zeros; f(-3) = 60 \r<BR>\n" );
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document.write( "A) f(x) =  6   + 24   + 6x  + 24 <BR>\n" );
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document.write( "B) <BR>\n" );
document.write( "f(x) = -6   - 24   + 6x  + 24  \r<BR>\n" );
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document.write( "C) <BR>\n" );
document.write( "f(x) =  6   + 24   - 6x  - 24 <BR>\n" );
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document.write( "D) <BR>\n" );
document.write( "f(x) = -6   - 24   - 6x  - 24 \r<BR>\n" );
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document.write( "I'm not sure if I'm supposed to substitute the values into the multiple choices to see which one works out.  Regardless, I would like to find the answer on my own without having to plug the values in.  Could you help me?  I looked in my algebra book but I couldn't find a section for this.   I would greately appreciate it if someone could give me some direction.\r<BR>\n" );
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document.write( "Thank you,\r<BR>\n" );
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document.write( "EJ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76037 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> EJ, let's start with what you know. <BR>\n" );
document.write( "Nth degree polynomial with n=3 means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your job is to find a,b,c,d with the rest of the information provided.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-4%29=0 ALIGN=MIDDLE  ALT=\"f%28-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28i%29=0 ALIGN=MIDDLE  ALT=\"f%28i%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=60 ALIGN=MIDDLE  ALT=\"f%28-3%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problems is you have 4 unknowns (a,b,c,d) and only three equations to solve them with. Let's plug in and see what we find. <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-4%29=a%28-4%29%5E3%2Bb%28-4%29%5E2%2Bc%28-4%29%2Bd=0 ALIGN=MIDDLE  ALT=\"f%28-4%29=a%28-4%29%5E3%2Bb%28-4%29%5E2%2Bc%28-4%29%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28i%29=a%28i%29%5E3%2Bb%28i%29%5E2%2Bc%28i%29%2Bd=0 ALIGN=MIDDLE  ALT=\"f%28i%29=a%28i%29%5E3%2Bb%28i%29%5E2%2Bc%28i%29%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=a%28-3%29%5E3%2Bb%28-3%29%5E2%2Bc%28-3%29%2Bd=0 ALIGN=MIDDLE  ALT=\"f%28-3%29=a%28-3%29%5E3%2Bb%28-3%29%5E2%2Bc%28-3%29%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the equations, gives you<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-64a%2B16b-4c%2Bd=0 ALIGN=MIDDLE  ALT=\"-64a%2B16b-4c%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-ia-b%2Bic%2Bd=0 ALIGN=MIDDLE  ALT=\"-ia-b%2Bic%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27a%2B9b-3c%2Bd=60 ALIGN=MIDDLE  ALT=\"-27a%2B9b-3c%2Bd=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E3=-i ALIGN=MIDDLE  ALT=\"i%5E3=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Since you have a complex expression in your second equation, it actually acts as an additional equation. Since both the real part and the complex part of equation 2 have to equal zero, you now have 4 equations with four unknowns.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-64a%2B16b-4c%2Bd=0 ALIGN=MIDDLE  ALT=\"-64a%2B16b-4c%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.(Real)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2Bd=0 ALIGN=MIDDLE  ALT=\"-b%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.(Complex)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bc=0 ALIGN=MIDDLE  ALT=\"-a%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27a%2B9b-3c%2Bd=60 ALIGN=MIDDLE  ALT=\"-27a%2B9b-3c%2Bd=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With those 4 equations, you are able to substitute and find the values for a,b,c,d. <BR>\n" );
document.write( "Good luck and post another question if you get stuck.  </SPAN>\n" );
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