document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132419>Question 132419</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( "5x2 + 8x + 7 = 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 #96754 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=96754\">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( "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=5x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"y=5x%5E2%2B8x%2B7\"   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=%288%29%5E2-4%2A5%2A7 ALIGN=MIDDLE  ALT=\"D=%288%29%5E2-4%2A5%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=5, b=8, c=7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=64-4%2A5%2A7 ALIGN=MIDDLE  ALT=\"D=64-4%2A5%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 8 to get 64\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=64-140 ALIGN=MIDDLE  ALT=\"D=64-140\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*5*7 to get -140\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-76 ALIGN=MIDDLE  ALT=\"D=-76\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 64 and -140 to get -76\r<BR>\n" );
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document.write( "Since the discriminant equals -76  (which is less than zero) , this means  there are two complex solutions (ie there are no real solutions). Remember if the discriminant is less than zero, then the quadratic will have two complex 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=5x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"y=5x%5E2%2B8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no 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=5x%5E2%2B8x%2B7 ALIGN=MIDDLE  ALT=\"y=5x%5E2%2B8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that there are no real solutions. So this verifies our answer.\r<BR>\n" );
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