document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131842>Question 131842</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780471659587/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Directions: Find a polynomial of minimum degree (there are many) that have the given zeros:   1-sqrt(13), 1+sqrt(13).  \r<BR>\n" );
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document.write( "I understand that if the zeros are: -2,0,2 then the polynomial would work out like this: x(x+2)(x-2)=x(x^2-4)=x^3-4x\r<BR>\n" );
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document.write( "But the whole square root thing is really throwing me off, if you could help, I would really appreciate it.  Thank you for your time. :o) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96268 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have it right.  Just look at your zeros, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-sqrt%2813%29 ALIGN=MIDDLE  ALT=\"1-sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%2813%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as if they were just numbers (which they are actually), and do what you would do with a number.\r<BR>\n" );
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document.write( "a is a root of the polynomial equation if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of the polynomial, so for your problem the factors are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%281-sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"x-%281-sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%281%2Bsqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"x-%281%2Bsqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-1%2Bsqrt%2813%29%29%28x-1-sqrt%2813%29%29 ALIGN=MIDDLE  ALT=\"y=%28x-1%2Bsqrt%2813%29%29%28x-1-sqrt%2813%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have to extend the FOIL process somewhat to multiply what are actually trinomials, but if you follow a pattern, it will all work out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-x-x%2Asqrt%2813%29-x%2B1%2Bsqrt%2813%29%2Bx%2Asqrt%2813%29-sqrt%2813%29-13 ALIGN=MIDDLE  ALT=\"y=x%5E2-x-x%2Asqrt%2813%29-x%2B1%2Bsqrt%2813%29%2Bx%2Asqrt%2813%29-sqrt%2813%29-13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now collect terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-2x-12 ALIGN=MIDDLE  ALT=\"y=x%5E2-2x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Done.\r<BR>\n" );
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document.write( "To check the answer, you can complete the square on the resultant polynomial:<BR>\n" );
document.write( "Set the polynomial equal to 0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-12=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put the constant on the right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x=12 ALIGN=MIDDLE  ALT=\"x%5E2-2x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide the first degree term coefficient by 2 and square the result, adding the result to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1=13 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2=13 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=sqrt%2813%29 ALIGN=MIDDLE  ALT=\"x-1=sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=-sqrt%2813%29 ALIGN=MIDDLE  ALT=\"x-1=-sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2813%29 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2813%29 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Answer checks. </SPAN>\n" );
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