document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161257>Question 161257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:\r<BR>\n" );
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document.write( "Use the discriminant to determine the number of real solutions of the equation.\r<BR>\n" );
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document.write( "7 + 5z^2 = 2z </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118845 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=118845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The discriminant for a quadratic equation is given by <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the equation is in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+%2B+5z%5E2+=+2z ALIGN=MIDDLE  ALT=\"7+%2B+5z%5E2+=+2z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rearrange the equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5z%5E2-2z%2B7=0 ALIGN=MIDDLE  ALT=\"5z%5E2-2z%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In your case, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=7 ALIGN=MIDDLE  ALT=\"c=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The discriminant is then, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-2%29%5E2-4%285%29%287%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%285%29%287%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%5E2-4ac=4-144 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=4-144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=-148 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=-148\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The discriminant gives you information regarding the roots depending on its value. <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3E0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have two distinct real roots.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have two coincident real roots.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have two complex roots (complex conjugates).<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=-148 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=-148\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you will have two complex conjugate roots. </SPAN>\n" );
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