document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469064>Question 469064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help! I asked earlier and I have tried but I do not even understand the question. Can someone please help me understand these two?<BR>\n" );
document.write( "Determine the nature of the solutions of the equations.<BR>\n" );
document.write( "y^2=1/5y+2/3<BR>\n" );
document.write( "x^2-4=0<BR>\n" );
document.write( "Is there one real solution, two real solutions, or two non real solutions?<BR>\n" );
document.write( "I believe that the first one has 2 real solutions and that the second one has two non real solutions. Did I even come close? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321943 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the nature of the solutions of the equations.<BR>\n" );
document.write( "y^2=1/5y+2/3<BR>\n" );
document.write( "x^2-4=0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You do this by using the rules of the discriminant<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation should be in the form ax^2 + bx + c<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The discriminant: d = b^2 - 4*a*c<BR>\n" );
document.write( "The rules,<BR>\n" );
document.write( "If d > 0 there are two distinct real roots (solutions)<BR>\n" );
document.write( "If d = 0 there is one real solution(a double root)<BR>\n" );
document.write( "If d < 0 there is two imaginary roots, one the conjugate of the other<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Put the 1st equation in ax^2 + bx + c form<BR>\n" );
document.write( "y^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >y - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then <BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "b=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F5 ALIGN=MIDDLE  ALT=\"-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%29%5E2 ALIGN=MIDDLE  ALT=\"%28-1%2F5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 4 * 1 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2F3 ALIGN=MIDDLE  ALT=\"-8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d > 0, therefore there are two distinct real roots, (the exact value is not needed) so you are right.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the 2nd equation is in ax^2 + bx + c form<BR>\n" );
document.write( "x^2 - 4 = 0<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "b=0<BR>\n" );
document.write( "c=-4<BR>\n" );
document.write( "d = -4*1*-4<BR>\n" );
document.write( "d = +16 > 0, also two distinct real roots<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can see that if you solve it<BR>\n" );
document.write( "x^2 -4 = 0<BR>\n" );
document.write( "x^2 = 4<BR>\n" );
document.write( "x = +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +2<BR>\n" );
document.write( "and <BR>\n" );
document.write( "x = -2 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );