document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297318>Question 297318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Studing solotions of quadratic equations.\r<BR>\n" );
document.write( "\n" );
document.write( "For each equation determine whether the solutions are real or imaginary. If they are real specify whether they are rational or irrational.\r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 3x - 6 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214140 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can graph it. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%2B3x-6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%2B3x-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Since it crosses the x-axis the solutions are real. <BR>\n" );
document.write( "Now use the quadratic formula,<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+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-6%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-6%29+%29%29%2F%282%2A1%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+=+%28-3+%2B-+sqrt%28+9%2B25+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9%2B25+%29%29%2F%282%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+=+%28-3+%2B-+sqrt%28+34%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+34%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since 34 is not a perfect square, the solutions are irrational.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );