document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132421>Question 132421</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the following equations have a solution or not? Justify your answer<BR>\n" );
document.write( "2x2 + x - 1 = 0 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96755 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=96755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  From the quadratic formula\r<BR>\n" );
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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" );
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document.write( "the discriminant consists of all of the terms in the square root. So the discriminant is\r<BR>\n" );
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document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.\r<BR>\n" );
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document.write( "Now let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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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;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%281%29%5E2-4%2A2%2A-1 ALIGN=MIDDLE  ALT=\"D=%281%29%5E2-4%2A2%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=1, c=-1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1-4%2A2%2A-1 ALIGN=MIDDLE  ALT=\"D=1-4%2A2%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1 to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1%2B8 ALIGN=MIDDLE  ALT=\"D=1%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*2*-1 to get 8\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=9 ALIGN=MIDDLE  ALT=\"D=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 1 and 8 to get 9\r<BR>\n" );
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document.write( "Since the discriminant equals 9  (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" );
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document.write( "So the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > has two solutions.\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"y=2x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that there are two real solutions. So this verifies our answer. \r<BR>\n" );
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