document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=686643>Question 686643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one of the questions to my homewok that i am having trouble with answering was r^2-3r/5+2/25=0 and the homework asks to find the value of the discriminant and describe the nature of the roots of each quadratic equation Then solve the equation and ive tried various ways but i have no confidence so o=if you can help that would be great </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424863 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=424863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you have the equation in 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;\" >, the 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 rules are:<BR>\n" );
document.write( "(1) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+%3C+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there are 2 imaginary roots<BR>\n" );
document.write( "(2) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+%3E+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there are 2 real roots<BR>\n" );
document.write( "(3) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+0+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there is a single real root ( called a double root )<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28r%29+=+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+ ALIGN=MIDDLE  ALT=\"+f%28r%29+=+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+=+0+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that this is saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28r%29+=+0+ ALIGN=MIDDLE  ALT=\"+f%28r%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which means that the<BR>\n" );
document.write( "values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > that you find will be the x-crossings which are the roots )<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The fact that you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't matter<BR>\n" );
document.write( "The form is still <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0+ ALIGN=MIDDLE  ALT=\"+a%2Ax%5E2+%2B+b%2Ax+%2B+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=+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+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+b+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+2%2F25+ ALIGN=MIDDLE  ALT=\"+c+=+2%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now just plug these into the discriminant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4%2Aa%2Ac+=+%283%2F5%29%5E2+-+4%2A1%2A%282%2F25%29+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+%283%2F5%29%5E2+-+4%2A1%2A%282%2F25%29+\"   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+=+9%2F25+-+8%2F25+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+9%2F25+-+8%2F25+\"   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+=+1%2F25+ ALIGN=MIDDLE  ALT=\"+b%5E2+-+4%2Aa%2Ac+=+1%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "This is a positive result, so there are 2 roots, and they are real<BR>\n" );
document.write( "Now to solve equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+=+0+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+2%2F25+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+r+-+2%2F5+%29%2A%28+r+-+1%2F5+%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28+r+-+2%2F5+%29%2A%28+r+-+1%2F5+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( I could see the result by inspection )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+2%2F5+ ALIGN=MIDDLE  ALT=\"+r+=+2%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+r+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the solutions<BR>\n" );
document.write( "But here's solution by completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+=+-2%2F25+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+=+-2%2F25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+%283%2F10%29%5E2+=+-2%2F25+%2B+%283%2F10%29%5E2+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+%283%2F10%29%5E2+=+-2%2F25+%2B+%283%2F10%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+-2%2F25+%2B+9%2F100+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+-2%2F25+%2B+9%2F100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+-8%2F100+%2B+9%2F100+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+-8%2F100+%2B+9%2F100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+1%2F100+ ALIGN=MIDDLE  ALT=\"+r%5E2+-+%283%2F5%29%2Ar+%2B+9%2F100+=+1%2F100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+r+-+3%2F10+%29%5E2+=+%281%2F10%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28+r+-+3%2F10+%29%5E2+=+%281%2F10%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "take the square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+-+3%2F10+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+r+-+3%2F10+=+1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+4%2F10+ ALIGN=MIDDLE  ALT=\"+r+=+4%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+2%2F5+ ALIGN=MIDDLE  ALT=\"+r+=+2%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But, also I can say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+-+3%2F10+=+-1%2F10+ ALIGN=MIDDLE  ALT=\"+r+-+3%2F10+=+-1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Taking the negative square root of (1/10)^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+3%2F10+-+1%2F10+ ALIGN=MIDDLE  ALT=\"+r+=+3%2F10+-+1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+2%2F10+ ALIGN=MIDDLE  ALT=\"+r+=+2%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+r+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I get the same answers<BR>\n" );
document.write( "I hope this helps\r<BR>\n" );
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