document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029915>Question 1029915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find p such that px^2-12x+4=0 has only one solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644850 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=644850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For there to be just 1 solution, the part<BR>\n" );
document.write( "of the quadratic formula called the <BR>\n" );
document.write( "discriminant must equal zero.<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 quadratic formula is:<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( "when you are given the general form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this is how you find a, b, and c<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "So, for 1 solution:<BR>\n" );
document.write( "<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;\" ><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( "------------------<BR>\n" );
document.write( "You are given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%2Ax%5E2+-+12x+%2B+4+=+0+ ALIGN=MIDDLE  ALT=\"+p%2Ax%5E2+-+12x+%2B+4+=+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+=+%28-12%29%5E2%0D%0A%7B%7B%7B+b%5E2+=+144+ ALIGN=MIDDLE  ALT=\"+b%5E2+=+%28-12%29%5E2%0D%0A%7B%7B%7B+b%5E2+=+144+\"   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=+4%2Aa%2Ac+=+4%2Ap%2A4+ ALIGN=MIDDLE  ALT=\"+4%2Aa%2Ac+=+4%2Ap%2A4+\"   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=+144+=+4%2Ap%2A4+ ALIGN=MIDDLE  ALT=\"+144+=+4%2Ap%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+9+ ALIGN=MIDDLE  ALT=\"+p+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+=+9+ ALIGN=MIDDLE  ALT=\"+p+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is only 1 solution<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "check the answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x%5E2++-+12x+%2B+4+=+0+ ALIGN=MIDDLE  ALT=\"+9x%5E2++-+12x+%2B+4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2+-+4%2A9%2A4+%29%29+%2F+%282%2A9%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2+-+4%2A9%2A4+%29%29+%2F+%282%2A9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+12+%2B-+sqrt%28+144+-+144+%29%29+%2F+18+ ALIGN=MIDDLE  ALT=\"+x+=+%28+12+%2B-+sqrt%28+144+-+144+%29%29+%2F+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+12+%2B-+0+%29+%2F+18+ ALIGN=MIDDLE  ALT=\"+x+=+%28+12+%2B-+0+%29+%2F+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2%2F3+ ALIGN=MIDDLE  ALT=\"+x+=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, there is only 1 solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );