document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134718>Question 134718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 3 question.<BR>\n" );
document.write( "1.How do you know if a quadratic equation will have one, two,or no solutions?\r<BR>\n" );
document.write( "\n" );
document.write( "2. How do you find a quadratic equation if you are only given the solution?\r<BR>\n" );
document.write( "\n" );
document.write( "3. Is it possible to have different quadratic equations with the same solution?\r<BR>\n" );
document.write( "\n" );
document.write( "This information is for my college algebra class.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks Roosevelt </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98548 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Look at the determinant part of the quadratic equation<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( "The determinant is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+ ALIGN=MIDDLE  ALT=\"sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "If that results in a negative == no solutions (complex numbers)<BR>\n" );
document.write( "If it is positive, then two roots<BR>\n" );
document.write( "If it is 0, the one root two times\r<BR>\n" );
document.write( "\n" );
document.write( "2) Lets say the solutions are x=5 and x= 7<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%28x-7%29+=+0+ ALIGN=MIDDLE  ALT=\"%28x-5%29%28x-7%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > will give a quadratic equation with those solutions<BR>\n" );
document.write( "More generally, if the roots are a and b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%28x-b%29+=+0+ ALIGN=MIDDLE  ALT=\"%28x-a%29%28x-b%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > then just multiply it out \r<BR>\n" );
document.write( "\n" );
document.write( "3)Sure. One quick way to see that is to just multiply by a constant C<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x-a%29%28x-b%29+=+0+ ALIGN=MIDDLE  ALT=\"C%28x-a%29%28x-b%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > same root, different equation\r<BR>\n" );
document.write( "\n" );
document.write( "make sense? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );