document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937988>Question 937988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to figure out how to find \"Complex Zeros of Quadratic Functions\" but the Holt McDougal video lesson isn't helping whatsoever and I've researched as much as I could. I'm trying to find the zeros of \"f(x)=x²+2x+3\" and the video says the answer is x=6+2i&#8730;3. This involves imaginary numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571338 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=571338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What happens if you put the function into a graph?\r<BR>\n" );
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document.write( "You can try the old slow way of making a data table for getting several points and then plotting them, and try to guess the ROOTS or ZEROS.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This parabola does not cross nor touch the x-axis, and therefore has NO REAL ZEROS.  \r<BR>\n" );
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document.write( "But the function DOES have Complex zeros.  <BR>\n" );
document.write( "Accept a number, i such that:<BR>\n" );
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document.write( "Raising this to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > power, you find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=-sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=-sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "NEXT,  set f(x) to 0, and SOLVE FOR x, using Completing the Square.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B%282%2F2%29%5E2%2B3=%282%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B%282%2F2%29%5E2%2B3=%282%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  the full expression shown so it will be less of a mystery<BR>\n" );
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