document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039805>Question 1039805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the discriminant to describe the roots of each equation. Then select the best description.\r<BR>\n" );
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document.write( "2 = x2 + 5x\r<BR>\n" );
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document.write( "double root<BR>\n" );
document.write( "real and rational root<BR>\n" );
document.write( "real and irrational root<BR>\n" );
document.write( "imaginary root </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654555 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+%2B+5x+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+%2B+5x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The general equation for a quadratic has the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+5+ ALIGN=MIDDLE  ALT=\"+b+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+0+ ALIGN=MIDDLE  ALT=\"+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+5%5E2+-+4%2A1%2A0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+5%5E2+-+4%2A1%2A0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+25+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "The discriminant is real and positive, and it is not zero<BR>\n" );
document.write( "also, the discriminant is a perfect square. When you <BR>\n" );
document.write( "plug the discriminant back into the quadratic<BR>\n" );
document.write( "formula, you have 2 real, rational roots<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Here's the plot of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+5x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+%2B+5x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );