document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1803>Question 1803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why are there usually two solutions in quadratic equations </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a quadratic is any equation of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y=ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where a, b, c are constants.\r<BR>\n" );
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document.write( "The largest power is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This ALWAYS gives a \"u\" or a \"n\" shaped graph. So, these shapes will cross the x-axis either 2 times, or perhaps just once or perhaps never...but NEVER more than 2 times.\r<BR>\n" );
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document.write( "Where the curve (equation) crosses the x-axis, these are the ROOTS, because here, we are saying at this/these point(s), y=0...what are the x-values.\r<BR>\n" );
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document.write( "Similarly, a straight line will cross the x-axis just once (or possibly never), but never more than once, so any straight line will have (usually) just 1 root..1 \"answer\".\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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