document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119529>Question 119529</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618106480/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> determine whether the equation has 2 solutions, 1 solution, or no solution.  SHOW WORK!  PUT IN STANDARD FORM!\r<BR>\n" );
document.write( "\n" );
document.write( "22)x^2-3x+2=0 <BR>\n" );
document.write( "24)-3x^2+5x-1=0<BR>\n" );
document.write( "26)x^2-2x+4=0<BR>\n" );
document.write( "28)3x^2-6x+3=0<BR>\n" );
document.write( "30)-5x^2+6x-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 #87595 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=87595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first two to help you get started\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#22\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " From the quadratic formula\r<BR>\n" );
document.write( "\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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the discriminant consists of all of the terms in the square root. So the discriminant is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-3x%2B2 ALIGN=MIDDLE  ALT=\"y=x%5E2-3x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-3%5E2-4%2A1%2A2 ALIGN=MIDDLE  ALT=\"D=-3%5E2-4%2A1%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-3, c=2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=9-4%2A1%2A2 ALIGN=MIDDLE  ALT=\"D=9-4%2A1%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -3 to get 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=9-8 ALIGN=MIDDLE  ALT=\"D=9-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*1*2 to get -8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1 ALIGN=MIDDLE  ALT=\"D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 9 and -8 to get 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the discriminant equals 1  (which is greater than zero) , this means  there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " From the quadratic formula\r<BR>\n" );
document.write( "\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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the discriminant consists of all of the terms in the square root. So the discriminant is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%5E2%2B5x-1 ALIGN=MIDDLE  ALT=\"y=-3x%5E2%2B5x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=5%5E2-4%2A-3%2A-1 ALIGN=MIDDLE  ALT=\"D=5%5E2-4%2A-3%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-3, b=5, c=-1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=25-4%2A-3%2A-1 ALIGN=MIDDLE  ALT=\"D=25-4%2A-3%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 5 to get 25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=25-12 ALIGN=MIDDLE  ALT=\"D=25-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*-3*-1 to get -12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=13 ALIGN=MIDDLE  ALT=\"D=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 25 and -12 to get 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the discriminant equals 13  (which is greater than zero) , this means  there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );