document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678342>Question 678342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FInd the value of c so that the equation will have exactly one rational solution.  \r<BR>\n" );
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document.write( "4p^2-12p+c=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421312 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%26%238722%3B+4ac ALIGN=MIDDLE  ALT=\"b%5E2+%26%238722%3B+4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be used to determine the number and type of solutions a quadratic equation has the following types of solutions\r<BR>\n" );
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document.write( "Discriminant....................................................Number and Type of Solutions<BR>\n" );
document.write( "Positive, and the square of an integer..............2 rational solutions<BR>\n" );
document.write( "Positive, but not the square of an integer.........2 irrational solutions<BR>\n" );
document.write( "Zero .....................................................................1 rational solution<BR>\n" );
document.write( "Negative..............................................................2 non-real complex solutions\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2-12p%2Bc=0 ALIGN=MIDDLE  ALT=\"4p%5E2-12p%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use discriminant to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+b%5E2+-+4ac ALIGN=MIDDLE  ALT=\"0+=+b%5E2+-+4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >....in this case we have 1 rational solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%2812p%29%5E2+-+4%2A4c ALIGN=MIDDLE  ALT=\"0+=+%2812p%29%5E2+-+4%2A4c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+144p%5E2+-+16c ALIGN=MIDDLE  ALT=\"0+=+144p%5E2+-+16c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16c+=+144p%5E2+ ALIGN=MIDDLE  ALT=\"16c+=+144p%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+144p%5E2%2F16+ ALIGN=MIDDLE  ALT=\"c+=+144p%5E2%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+9p%5E2 ALIGN=MIDDLE  ALT=\"c+=+9p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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