document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530526>Question 530526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2%2B2x%2B3=0+ ALIGN=MIDDLE  ALT=\"+2x%5E2%2B2x%2B3=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, explain how to find a value of \"b\" where the discriminant yields a quadratic equation with the following types of solutions.\r<BR>\n" );
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document.write( "a. two imaginary solutions\r<BR>\n" );
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document.write( "b. one real solution\r<BR>\n" );
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document.write( "c. two rational solutions\r<BR>\n" );
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document.write( "d. two irrational solutions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350125 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=350125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant is <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( "where <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;\" ><BR>\n" );
document.write( "In the quadratic formula, it appears<BR>\n" );
document.write( "under the square root sign<BR>\n" );
document.write( "(1) <BR>\n" );
document.write( "2 imaginary solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+%3C+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+%3C+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "1 real solution:<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( "(3)<BR>\n" );
document.write( "2 rational solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+%3E+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+%3E+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<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;\" > is a perfect square<BR>\n" );
document.write( "(4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+%3E+4%2Aa%2Ac+ ALIGN=MIDDLE  ALT=\"+b%5E2+%3E+4%2Aa%2Ac+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <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;\" > is not a perfect square </SPAN>\n" );
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